Seeing as he didn't actually see Cedric die (no, he didn't, JK. You explicitly told us he shut his eyes and saw green light through his eyelids), he shouldn't have seen thestrals for the first time at the start of fifth year. If he was going to see them at all, it should have been the first time he was in their presence, full stop. Why couldn't he have seen his mother die? She was standing in front of him and yelling, he sure wouldn't be looking anywhere else.
He took boats into school at the beginning
and end of first year, he flew in with a car at the beginning of his second year, and why the hell not invent a reason to have him miss the thestrals and carriages at the end of second year? He couldn've encountered thestrals for the first time at the beginning of his first year, right after seeing the dementors. It's not as if the fifth book particularly belabours Harry seeing things others can't over any other book - in CoS he hears voices nobody else can hear, in PoA he hears screams nobody else can hear and responds particularly poorly to dementors, in GoF everybody doubts his innocence about putting his name in the goblet and the tabloids imply bad things about him, and
then in OoP he has visions and the Ministry is badmouthing him. Just saying, they didn't need to appear in
that book to be an extra serving of "Am I crazy?" pie, because he's been glutting on it for years.
(And if he didn't see his mother die, he
heard it and saw the light - that's explicitly in the books - so had the
exact same conditions as his witnessing Cedric's death. Yes, I HAVE thought about this too much.)