Does anyone know when summer PhD research internship applications are reviewed by big companies? Is it on a rolling basis?

For context, I'm a 3rd year PhD student in a decent program (top 20-40 using the rankings) in the US with a handful of good first-author publications. In November/December I applied to over 20 research science summer internships at a wide range of companies, including a couple of companies where I met a few people at research conferences I attended this year. I have only heard back (with negative answers) from 2 companies so far, and I'm wondering if I'll just be ghosted this year? Or maybe it's too early to worry about responses? I did take and pass one online codeforces-style interview a couple weeks ago, but I haven't heard back from that company either.

I know the best way to get an internship is to connect with people -- I'm trying my best, but as an early-career researcher from a not-famous lab it's a little hard to make connections!