Dear OP,
It is almost certainly not the post office's problem here.
Very common ID theft is just stealing mail from unlocked boxes. And, it is not difficult to "spoof" a phone number when calling to activate a card (do you have a listed number? Or could it be found in a second on goggle?).
Please, do yourself a favor and get a secure, locked box.
My box at home is unlocked and not secure. Because all that goes there is junk mail. Otherwise, everything goes to a locked box at the Post Office.