Advice: should I wait for a referral or should just apply without one?

I’m applying for a job at Verve Therapeutics, and the person I reached out to for a referral (an old coworker) still hasn’t seen my message on LinkedIn. Since the position was posted less than 48 hours ago and already has over 100 applicants, should I keep waiting for her reply, or should I go ahead and send my application without a referral? Given how competitive things have been, I was really hoping to get this referral, but I also don’t want to wait too long and risk the position closing before I apply as some postings close within just a few days. Just as an FYI:

1. I saw the position the day it was posted and sent my message that same day, though it was pretty late, so I decided to wait another day.
2. My background matches the requirements perfectly.