Comment by sandinmyjoints

There's a book Debt: The First 5000 Years (by the David Graeber that parent commenter references several times) that observes that there’s no documented case of a society that ran mainly on barter and then invented money to escape it. The "barter first, then money" story is mostly a thought experiment. I'm not in a position to confirm or refute this based on my own knowledge or to do the research to develop that knowledge, but I'm not aware of anyone seriously challenging Graeber on this point.

IIRC, Graeber suggests that debt comes first. Initially it is tracked by memory, then when that gets too complicated, some kind of item is chosen to represent debt, which then in some cases evolves into currency. I believe this process has been observed.