Waiting for a referral or applying right away?

I’ve reached out to employers on LinkedIn who work at the company I'm applying to, but it sometimes takes a few days for them to get back-if they do at all. A referral is often times the best way to get your foot in the door, but at the same time, I don't want to wait too long before I apply and the listing has 10000 applicants. Which one would you do? For example I know Amazon best chance is to apply and complete the OA early. If I wait 1-3 days for an Amazon referral, would that hurt my chances ?