Money predates governments, though, and there are many examples of successful money that did not require a government to prop it up. Consider e.g. https://en.wikipedia.org/wiki/Shell_money or https://en.wikipedia.org/wiki/Rai_stones.

Note that in the latter case, the physical money doesn't even change hands - it's all in a ledger, but the ledger is in people's heads. In fact, you could say it's a proof-of-work system, since making the stones is expensive in terms of amount of effort spent, even though they don't have any utility as such.