I would hope they have it somewhere in the local area. But, I would expect any given branch to only have a little more than they normally need for typical days business for security reasons.
Typically they get a delivery from the nearest federal reserve branch, usually the state capital or other large city, daily. Usually very early before the branch opens.
my wife used to work as a teller part time after highschool. It’s kind of interesting how things are done versus how people perceive them to be done