Honest question: does it matter if I'm currently working at a no-name startup vs a well-known company?

I've been at a 20-person startup for 3 years. Good experience, lots of ownership, but nobody has heard of us. When I look at LinkedIn profiles of people at Google/Meta, most of them came from other well-known companies.

Is there a bias in hiring? Should I first move to a mid-tier company (like a Series C/D startup) before trying for FAANG?

I know technically the interview is supposed to be a level playing field, but curious about people's real experiences.