Although people he’s met don’t remember him, etc. Peter Parker didn’t get erased from existence. He still has access to whatever $$ he had, and maybe even whatever May left. We know he was planning on going to MIT. Maybe, like MJ, he too had a side job to put money aside that we just never saw. Repairing computers on the side, or something.
The place didn’t look particularly nice, and maybe by the time of a sequel he’ll have realized that he needs a roommate to help cover rent—New York City is expensive!