If you actually are talented, and reasonably right for the role: figure out who the hiring manager is and message them on LinkedIn. You don't have to make sure it's the right HM, as long as you're close they'll point you in the right direction.

I've done this many times (before working in big tech) and I have always received a response. There is only 1 company that I've failed to get through for at least some kind of a screen: MSFT. They seem to want nothing to do with me.

I is frustrating from our side too. My boss just sent me a half dozen resumes: they all look the same to me: someone fresh out of a CS degree looking for a job (this is an entry level position so that is what we want). I really don't want to interview 6 people for one position, so who do we call in?

The "fair" and probably also reasonable imo thing to do is just pick randomly if you have a bunch of equally good people and can't interview them all.

Or make them do leetcode stuff, I think this situation is basically what that whole part of the process is for.