My college daughter tested positive on a Monday, symptoms started on Saturday, and health services wrote her a letter on Friday when she was out of isolation but masked (after many email exchanges trying to explain why she wants one...was surprised they actually did it). I'll find out in a couple days if Safe Passage will accept it.
People have said a letter at 5 or 10 days, (or longer) after positive test are ok--symptoms should be improving/fever gone before seeking letter. Needs to be signed, on medical letterhead with phone #/address, say cleared to travel, list patients date of birth, and positive test. You do need a copy of the positive test result as well, can't be an unproctored home antigen test.