You can get a PO Box or mailbox at your local postal store. Not the post office, because the lines are usually eternally long. However, if you go to a mom-and-pop postal store, you'll be able to get one. Then you can sign up online for a Chime or similar banking account.
I helped my niece sign up for a Chime account and it was super simple. It's all done online, so you don't have to go to a bank. You won't go through a credit or background check. Chime sends two cards, a credit card and a debit card. The cards only work if you have money in the account.