It seems that much about that question depends on the definition of bank robbery and bank. Some sources (like this one: https://www.carpentershall.org/americas-first-bank-robbery) give earlier examples of bank robberies even in the United States. But the example given in this source is about a theft not an (armed) robbery, if one wants to make that distinction.

But the true definition you would need to make is what constitutes a “bank” to be robbed. Would you accept the temples of Ancient Greece as banks? If so, I’m pretty sure that there will have been plundering and looting of those even before 1 AD. Or do you need a counter, a teller and a safe?

I’m very interested if someone can find examples of robberies (or armed plundering) of banks from ancient times or 14th century or later Europe. The thing is, the popular cultural image of a bank robber is coined by the Western movies and Jesse James and Co.