Incidentally, I think applying for YC is one of the best ways for those without connections / pedigree. The nature of the application process is such that partners and YC alum reviewers usually look most closely at what the team has actually done, not merely what school they went to or what fancy startups the founders have worked at.

(I no longer work at YC, so I'm just speaking to my time working with 10 batches there.)