It seems that it started as a simple trade mechanism in the west. The earliest physical evidence is from Lydia (modern Turkey, minus the easternmost part) from the middle of the 7th century BC. Sources suggest that the first examples were from around 700 BC.

Most metals were traded in ingot form, most prominently copper and bronze. But precious metals are a different thing. You don't want an entire ingot of gold, because you're not going to be working with much gold at that time. You'll hammer it into fine jewelry, thin vessels, and gold leaf.

So rather than form ingots, they made much smaller slugs of gold (and in this area, electrum). The slugs would be a standard weight. But you can easily cheat on precious metals, and people still do all the time. You take a zinc slug and wrap it with gold. So it's a sketchy prospect. The king of Lydia (it's attributed to Croesus) then stamped his slugs with his seal, which offered assurance to traders that they were getting the real deal at the right weight.

From there, trade in precious metal as currency just makes sense. Wealth becomes easier to store, keep track of, keep secure, and hoard. It allows you to more easily address shortages and surpluses. And it's easier to work with when it comes to fluctuations in relative value of commodities based on those shortages and surpluses.

As far as I know, the actual moment in which metal slugs became formal currency, but the concept spread rapidly after that initial stamping in Lydia. And forgers and coin clippers followed shortly after.