Early application vs Referred Application

Hi all- I’m about to graduate soon from my grad school program and I had a question about applying. Is it better to apply early without a referral or later with a referral?

I believe it to be the latter, but dming people on LinkedIn and waiting is giving me a sense of no control which I don’t like. I have gotten a few responses from alumni’s at companies who work where I am applying, but lately I haven’t been getting much responses. I once got advice to use one email to apply early and that if I got a referral then use another one, but this kind of stuff has been patched in some applications as it happened to me in TikTok. I applied thinking I wouldn’t get a referral but then I do, so when I tried using another email, it wouldn’t submit.

As application deadlines approach, I’m trying to strategize accurately.