Right now we're in a weird place - if you have a network, you're pretty well off. If your network isn't hiring, or you are early in your career, it's brutal trying to get through the noise.
The truth is that proof of work matters. But the big problem is that proof of work is easy to fake right now. It takes being creative. I get a few emails a month right now. Honestly, I think this isn't going to work at this point - some go to my personal and some go to my professional emails. But what might work?
Look at people who are writing blogs. Is there something interesting on their blog? Is that worth engaging them on first? (I mean, don't waste their time if you aren't interested or if you're going to submarine it the second or third email - someone will feel used - but showing a dual purpose of the email might not be the worst thing and even if they don't have a position or influence on the position, you might have a good conversation.
Are you involved on bluesky/twitter/threads? Are you getting positive engagement? Are you finding ways to make community? It may not get the formal referral but it might make the social referral and give you 30 extra seconds with the resume and a reason to say yes.