[Bahamut]

I dunno, I had no problem getting into big companies and excepting my current company (a FAANG), I have only worked for small companies in my whole career (almost 5 years of working at small companies).

The big things that seem to matter are your experience, and interview performance. People at big companies come from all walks of life as well as small companies, there really isn't that much of a difference in that regard. As someone currently interviewing candidates, I really don't care if someone worked for a small company or big one - I mainly care if someone made the most of that experience.