In university (which I paid for myself through internships + loans), my cofounder and I just started coding on an idea, which got us into YC, which helped us get in front of a bunch of VCs, which allowed us to raise $3m in seed funding. No connections, just lots of googling and talking/pitching to anyone that would pay attention to us.
It could've been the 5% luck you're talking about, but certainly don't think that coming from a well-connected family is the only way to fundraise in 2021.