He did mention having an uncle who left him some money. While I doubt it was as much as his parents would have were he the son they wanted, I'd imagine it's enough for a Firebolt. We're told that's a lot of money, but a lot of money by Harry's standards as a 13-year-old or to the Weasleys isn't that that much to someone who came from a wealthy family, even if he only had what his uncle gifted him.