It comes to mind an experiment carried in France where they sent fake housing applications where the only difference between two sets of applicants was a Muslim-sounding name vs a Christian one. The results showed a much higher response rate for the latter, despite everything else being equal. I can't find the original, but found this similar one working with job applications (https://www.pnas.org/content/107/52/22384).
Not to negate the main point about "showing up", but there's more to it. When I've had the chance to hire someone and there are two similar candidates, I preferred to choose the one with the lower ranked school credentials. My thinking is that if this person has reached the same level of achievements with less environmental help, they probably have more grit and get-it-done in them than the candidate from the top school. Much more than that can be done in a systemic way, but it's a start.