What’s often considered to be the first recorded issuance of government-backed paper money in the Western world was in Colonial America, and it was quite by accident.
There had been precedents, but they were very limited, and we only know about them through historical records. Paper money tends to disappear in the archaeological record, while coins survive, which means that earlier experiments in paper money may simply be lost to history.
Repeatedly in the European records we find mention of money made from leather during times of warfare and siege. Reports indicate that European monarchs occasionally used paper money during periods of crisis, usually war, and they do maintain that in Catalonia and Aragon, James I issued paper money in 1250, but no known examples have survived. Then, when the Spanish laid siege to the city of Leyden in the Lowlands in 1574, Burgomeister Pieter Andriaanszoon collected all metal, including coins, for use in the manufacture of arms. To replace the coins, he issued small scraps of paper.
On July 1661, Sweden’s Stockholm Bank issued the first bank note in Europe to compensate for a shortage of silver coins. Although Sweden lacked silver, it possessed bountiful copper resources, and the government of Queen Christina (1634-1654) issued large copper sheets called platmynt (plate money), which weighed approximately 4 pounds each. In 1644 the government offered the largest coins ever issued: ten-daler copper plates, each of which weighed 43 pounds, 7 1/4 ounces. To avoid having to carry such heavy coins, merchants willingly accepted the paper bills in denominations of one hundred dalers. one such bill could be submitted for 500 pounds of copper plates. (Weatherford, p. 130)
For an example of platmynt, see this link: Swedish “plate money” (TYWKIIDBI)
The issuance was by Massachusetts in 1690. It was in the form of government IOU’s issued to pay for a failed raid on Quebec which was successfully repelled. Due to the failure of the raid, the expected booty to pay for the cost of the expedition did not materialize. The government, reluctant to raise taxes to pay for an expedition that was a failure, issued IOU’s instead. Due to the shortage of metal coins, these IOU’s began circulating at their face value as a substitute for coins. And thus, by accident, paper money was created in the Western world:
The first issue of paper money was was by the Massachusetts bay Colony in 1690; it has been described as ‘not only the origin of paper money in America, but also in the British empire, and almost in the Christian world’. It was occasioned, as noted, by war.
In 1690, Sir William Phips – a man whose own fortune and position had been founded on the gold and silver retrieved from a wrecked Spanish galleon near the shores of what is now Haiti and the Dominican Republic – led an expedition of Massachusetts irregulars against Quebec. The loot from the fall of the fortress was intended to pay for the expedition. The fortress did not fall.
The American colonies were operating on negligible budgets…and there was no enthusiasm for levying taxes to pay the defeated heroes. So notes were issued to the soldiers promising eventual payment in hard coin. Redemption in gold or silver, as these were returned in taxes, was promised, although presently the notes were also made legal tender for taxes. (Galbraith, pp. 51-52)
The colonial government intended to quickly redeem the certificates with tax revenues, but the need for money was so great that the certificates began changing hands, like money……For the next twenty years the notes circulated side by side with gold and silver of equivalent denomination. Notes and metal being interchangeable, there was pro tanto, no depreciation. (p. 52)…
The practice quickly caught on among the colonies as a means of supplying a circulating currency. The issuances were to be temporary, in fixed amounts, and accompanied by taxes and custom duties to redeem them. 
To retire these bills on credit, the colonial governments accepted them—along with specie—in payment of taxes, fines and fees. As with “bills on loan” the governments used any specie that they received in tax payments to retire and then burn the notes. Also like “bills on loan,” the notes circulated freely within the colonies that issued them and sometimes in adjacent colonies. 
This circulation of these paper IOUs gave cash-strapped governments an idea. Governments could issue IOUs (hypothetically redeemable in gold and silver coins) in lieu of levying taxes to enable the government to pay for stuff. Such IOUs could then circulate as cash money—valuable because they would theoretically be redeemed by governments for gold and silver, or be used to discharge debt obligations to the state like taxes, fines and fees. As noted above, when gold and silver did come into the state’s coffers, they could buy back the notes.
Unlike modern paper money, these IOUs typically had an expiration date. By redeeming the issued notes, the government could remove paper from circulation, lowering its debt obligations, while at the same time preventing paper money from losing too much of its value. (Note similarities with the Chinese system).
And so, as the 1700’s dawned, colonial governments started commonly issuing paper money—colonial scrip—in lieu of taxes to goose the domestic economy by increasing the amount of money in circulation. Since precious metals were in short supply, most of these schemes were based on the land banking concept (i.e. monetizing land):
The Pennsylvania legislature issued its first paper money in 1723 — a modest amount of £15,000 (the equivalent of just over 48,000 Spanish silver dollars), with another £30,000 issued in 1724. This paper money was not linked to or backed by gold and silver money. It was backed by the land assets of subjects who borrowed paper money from the government and by the future taxes owed to the government that could be paid in this paper money…after the legislature issued this paper money, internal trade, employment, new construction, and the number of inhabitants in the province all increased…The initial paper money issued in 1723 was due to expire in 1731. (Typically, paper money was issued with a time limit within which it could be used to pay taxes owed to the issuing government — the money paid in being removed from circulation.)
Benjamin Franklin and the Birth of a Paper Money Economy (PDF)
In addition to funding military spending, one major driver behind colonial governments issuing IOUs as currency came from the extreme recalcitrance of the colonists in paying their allotted taxes, which means that this unfortunate tendency was present in America from the very beginning, as Galbraith notes:
A number of circumstances explain the pioneering role of the American colonies in the use of paper money. War, as always, forced financial innovation. Also, paper money…was a substitute for taxation, and, where taxes were concerned, the colonists were exceptionally obdurate; they were opposed to taxation without representation, as greatly remarked, and the were also, a less celebrated quality, opposed to taxation with representation. ‘That a great reluctance to pay taxes existed in all the colonies, there can be no doubt. it was one of the marked characteristics of the American people long after their separation from England.’ (Galbraith, pp. 46-47)
In subsequent years, the various colonial governments would rely on more and more on issuing paper money. And when they did, it was noted, the volume of trade increased, and local economies expanded. There was always, however, the looming threat of too much colonial scrip being issued by governments, leading to depreciation:
Inevitably, however, it occurred to the colonists that the notes were not a temporary, one-time expedient but a general purpose alternative to taxation. More were issued as occasion seemed to require, and the promised redemption was repeatedly postponed.
Prices specified in the notes now rose; so, therewith did the price of gold and silver. By the middle of the eighteenth century the amount of silver or gold for which the note could be exchanged was only about a tenth of what it had been fifty years before. Ultimately the notes were redeemed at a few shillings to the pound from gold sent over to pay for the colonial contribution to Queen Anne’s War.
Samuel Eliot Morison has said of the notes issued by Massachusetts to pay off the soldiers back from Quebec that they were ‘a new device in the English-speaking world which undermined credit and increased poverty’. Other and less judicious historians have reflected the same view. But it is also known that rising prices stimulate the spirits of entrepreneurs and encourage economic activity just as falling prices depress both.
Were only so much paper money issued by a government as to keep prices from falling or, at most, cause a moderate increase, its use could be beneficial. Not impoverishment, but an increased affluence would be the result.
The question, obviously, is whether there could be restraint, whether the ultimate and impoverishing collapse could be avoided. The Law syllogism comes ominously to mind: If some is good, more must be better. (Galbraith, pp. 52–53)
The use of paper money as an alternative to government borrowing began to spread. More and more colonial governments (there obviously was no national government back then) would issue IOUs as a way to get around chronic shortages of gold and silver coins, and to avoid raising taxes. Meanwhile, although Europe had begun to experiment with paper money, it was still tied to amounts of gold and silver, limiting its application.
The results in the colonies were highly mixed. Some experiments were highly successful; other less so:
…the other New England colonies and South Carolina had also discovered paper money…Restraint was clearly not available in Rhode Island of South Carolina or even in Massachusetts. Elsewhere, however, it was present to a surprising extent. The Middle Colonies handled paper money with what must now be regarded as astonishing skill and prudence…The first issue of paper money there was by Pennsylvania in 1723. Prices were falling at the time, and trade was depressed. Both recovered, and the issue was stopped.
There appear to have been similar benefits from a second issue in 1729; the course of business and prices in England in the same years suggests that, in the absence of such action, prices would have continued down. Similar issues produced similarly satisfactory results in New York, New Jersey, Delaware and Maryland. As in Pennsylvania, all knew the virtue of moderation. (Galbraith, pp. 52-53)
Perhaps the most intriguing experiment was done by the state of Maryland. It had a combination of what looks like a UBI scheme, coupled with a public banking system (à la North Dakota):
The most engaging experiment was in Maryland. Elsewhere the notes were put into circulation by the simple device of using them to pay public expenses. Maryland, in contrast, declared a dividend of thirty shillings to each taxable citizen and, in addition, established a loan office where worthy farmers and businessmen could obtain an added supply which they were required to repay.
Remarkably, this dividend was a one-time thing; as in the other Middle Colonies the notes so issued were ultimately redeemed in hard money. A near contemporary historian with a near-gift for metaphor credited the experiment with ‘feeding the flame of industry that began to kindle’. A much later student has concluded that ‘this was the most successful paper money issued by any of the colonies’.
Two centuries later during the Great Depression a British soldier turned economic prophet, Major C.H. Douglas, made very nearly the same proposal. This was Social Credit. Save in much distant precincts as the Canadian Prairies, he acquired general disesteem as a monetary crank. He was two hundred years too late. (Galbraith, pp. 53-54)
Interestingly, we see some of those ideas once again being floated once again today.
As Galbraith notes, later economic historians would focus exclusively on the failures of such early experiments, and deliberately ignore the places were it was successful. Much of this was based on the “gold is real money” ideology, along with the ideas around the “inherent profligacy of governments” which would invariably cause inflation. In other words, the groupthink of the economics priesthood:
Towards the end of the nineteenth century expanding university facilities, an increased interest in the past and a pressing need for subjects on which to do doctoral theses and other scholarly research all led to a greatly expanded exploration of colonial economic history. By then, among historians and economists, the gold standard had become an article of the highest faith. Their research did not subordinate faith to fact.
By what amounted to a tacit understanding between right-thinking men the abandoned tendencies of Rhode Island, Massachusetts and South Carolina were taken to epitomize the colonial monetary experience. The different experience of the Middle Colonies was simply ignored.
A leading modern student of colonial monetary experience has noted that: ‘One looks in vain for any discussion of these satisfactory currency experiments in the standard works on American monetary and financial history.’ Another has concluded that ‘…generations of historical scholarship have fostered a mistaken impression of the monetary practices of the colonies’. (Galbraith, pp. 54-55)
History repeats itself: today we once again have an economics caste wedded to orthodoxy and unwilling to consider alternative points of view. The MMT school of economics is fighting a lonely battle against this tendency today.