Is there still a chance for people to get into prestigious schools if they have low AP Test scores?

I was wondering if it’s possible to get into universities like Princeton, Stanford, Columbia, etc. if you have poor AP test scores? I read that AP Test scores don’t really have a very big impact on admissions (they are mostly just used for getting credit), and I was wondering if it would look good to these universities if your AP Test scores improve from the first time you took the test? Like if in sophomore year you took an AP Test, got a 3, but took more AP Tests as a junior and got several 5s and a few 4s that year. Will this look good?

No. You don’t even have to report them, although it won’t look that good. They are not going to analyze it like grades going up. Worry about your grades and SAT I and II instead.