Thestrals

If you recall, thestrals can only be seen sa pamamagitan ng those who have seen death. Lucky for you, I was just compiling somenotes on them.
Harry doesn't remember anything of his parents' deaths except the light and the laugh. He was only a baby, after all. When we are babies, we have almost no capacity to hold memories. Try remembering what you were doing at that age. Impossible, isn't it?
Also, Harry watched Cedric die right in front of his face. Remember, he had nightmares about it for weeks, if we'er going sa pamamagitan ng Dudley's insult.
It's simple psychology that kept Harry from seeing them sooner. If you'd like a madami detailed explanation, I suggest asking your local psychology teacher.