Harry Potter question: Why couldn't Harry see the thestrals until Order of the Phoenix?

It was established pretty early on in the Harry Potter series that he was with his mother when Voldemort killed her. Harry saw the thestrals for the first time in Order of the Phoenix (after watching Cedric die in Goblet of Fire). We learn in Order of the Phoenix that, in order to see thestrals, one has to have seen death. If Harry witnessed his mother’s death when he was a baby, shouldn’t he have been able to see the thestrals all along?