I know for a while the rumors were basically that if you hadn't gone to a place like Stanford, you weren't getting a job, at least at Google (Maybe Facebook too?)
Is this still the case? (Was it ever the case, or were things a more flexible?)
If you have experience already, where you went to school gets dramatically less important the more experience you have. I went to a decent (but definitely not top tier) state school and have 15 years experience, had no trouble getting interviews at FAANG companies and passed interviews at a few.
This is at all relevant only for getting into the interview process, which is something that is largely handled by recruiting. Once a candidate makes it to a phone screen with someone like me, where they went to school has no bearing on whether they move forward in the process.