I wasn't aware that "elite of the elite" included many public schools that aren't even that difficult to get into. If you're a California resident UCSD, UCI, UCB, UCLA, UCSB are all accessible schools that give you a very solid shot at a FAANG job out of college. If you're a Michigan resident, same goes for UMich. Illinois, UIUC. Georgia, Georgia Tech. Texas, any number of great state schools. These schools are not that difficult to get into. They're also public, so there is no legacy shenanigans happening to boost wealthy applicants.

If you grew up in a shitty high school, you can go to a community college and then transfer to one of these state schools. I know for certain California has excellent policies that favor CC applicants transferring in. There are multiple ways in the door if you apply yourself.

Perhaps consider that a student that can't even get into a state school has no business or ability to write code at a level that would merit a 250k salary. The bar is on the floor.