Lots of banks don't have a ton of cash in their vaults anymore. If you want say 100 they have to order the cash to deliver to the bank. That's just a number I threw out. But you get my drift. The money you deposit is not kept where you deposit.
Do a little look into Fractional Reserve Banking. We can thank the Federal Reserve and what was created at Jekyll Island a century ago. An interesting read is The Creature from Jekyll Island.