I terms of working for a FAANG, in order to pass the interview, you have to first get the interview. If you attend Stanford, Berkeley, MIT, etc, FAANG's will have career fair booths, and lots of other opportunity for internships and networking. You will be at the top of the pile and you're almost guaranteed a look.
Contrast that to attending a school like SUNY Buffalo. FAANGs don't generally recruit from schools like that. When I worked for Google, I offered to help with recruiting from SUNY Buffalo (which they called a "long tail" school). Their response was, rather than send people to the school, they set up a giant hangouts/meet video chat with auditoriums of kids from 4 different schools. The especially irritating thing to me was that my alma mater was not even included in the session that I led.
I think this sucks because I went to SUNY Buffalo because they offered me a much, much better deal financially than the "elite" schools did. I could have attended one of the favored few, but decided that I'd rather graduate without massive debt. Some of the smartest people I know I met there. They definitely weren't the rule, but a lot went on to get PhD's from places like Stanford and Caltech. So its not like big state schools have no qualified candidates. Its just hard to get the FAANGs to see that.