What is the absolute earliest example of a "fiat currency" system that was accepted by a large group of people? To clarify, it doesn't have to be a national currency per se but I'd prefer something used in at least a notable city state that traded with other peoples. And by "fiat currency" I don't only mean a paper money system with a central bank, but in general the trading of items/coins that had low or nil intrinsic value based on the understanding that the issuing government would ensure the value of those coins going forward.
The earliest fiat money would almost certainly be Chinese paper money, which was first introduced in the 11th century.
In the 14th century, Marco Polo wrote about this currency in his Travels of Marco Polo:
In this city of Kanbalu is the mint of the Grand Khan, who may truly be said to possess the secret of the alchemists, as he has the art of producing money by the following process: He causes the bark to be stripped from those mulberry trees, the leaves of which are used for feeding silk-worms, and takes from it that thin inner rind which lies between the coarser bark and the wood of the tree. This being steeped and afterwards pounded in a mortar, until reduced to a pulp, is made into paper; resembling (in substance) that which is manufactured from cotton, but quite black. When ready for use he has it cut into pieces of money of different sizes, nearly square, but somewhat longer than they are wide. Of these, the smallest pass for a denier tournois; the next size, for a Venetian silver groat; others for two, five, and ten groats; others for one, two, three, and as far as ten besants of gold. The coinage of this paper-money is authenticated with as much form and ceremony, as if it were actually of pure gold or silver.
However, outside of relatively rare economic emergencies like gold and silver shortages, fiat money wasn't introduced on any large scale anywhere else until the 1660s when paper money called "credit paper" was issued by a bank in Stockholm to facilitate long-term loans that couldn't be covered by the bank's short-term deposits.
Although this scheme soon failed when the bank overextended itself and sparked a bank run (and Johan Palmstruch — the Dutch banker who came up with the scheme — ended up in jail for almost the rest of his life for his role in the shady bookkeeping) the practice of fractional reserve banking soon took off in Europe, spearheaded by English banks in the 1690s. This helped fuel the rapid expansion of colonial markets and was a major milestone on the road from the mercantilism of the early Age of Exploration to the capitalism of the Modern era.