"where would it be placed into the system?"
At the ATM machine.
That implies you have sufficient people in positions to get the cash into the machines - security-type jobs - and in multiple locations. Lithuanian job was a $100 bill, and ATMs dispense 20s. Not shooting it down completely, just testing it to the limit.
I don't mean just ATMs..but I do mean at the most basic point of distribution when possible. ATMs are in the stores now...it would be spread on Main Street. Also it could easily be spread in the illegal drug trade and in the Salvation Army kettles.
People have been known to deposit cash into ATMs...although I never would.
Pay for things with the money, dollar stores, Walgreens, any retailer etc will circulate it to the masses