We know HP's born on July 31, 1980, there's overwhelming fan-directed and Rowling-based evidence, along with pretty transparent clues.
But then, I reread the chapter of his 11th birthday (here is a timeline), and the text details the Dursley's trip day after day of the week, but as far as I can tell, the only absolute time frame for these events is "one day in July". There's a massive hint in the Hogwarts letter about "awaiting his owl by no later than 31 July" [which happens to be that very day], but that's no knowledge foundation either.
Is his exact birth date ever mentioned explicitly in the books?