My primary mechanism was reaching out to recruiters and people on LinkedIn that already had the jobs I wanted. I found that just applying through the job site almost never went anywhere. It comes down to a numbers game, so I would sort your hypothetical list of jobs from "dream job" at the top to "I guess" at the bottom, and then start applying from top down. You should absolutely take job postings and required skills with a healthy grain of salt. These are almost always generic, copy/paste artifacts.

An exception might be if you see "Publications in top-tiered journals" as a requirement. Those positions likely actually target PhDs with relevant publications. They might overlook a lack of a PhD if you're a recognized expert in the field, of course. But I interpret this requirement as "we want an academic", and there primary job is likely research and publishing papers. A Research Scientist at AWS is not an academic, as someone at Google Brain might be, but rather someone building applied ML solutions.

When they say they want a PhD, what they're really saying is that they want someone with a proven track record of generating and finishing their own researching projects, publishing top-tier papers, and who knows the state of the art in the field. Because you can't graduate from a PhD without that.

But if you happen to have those things without a PhD, then do apply anyway and I'm pretty sure they'll be interested.

If you don't have those things, then you may not be ready for these kinds of jobs.

There are several very successful academic and industrial CS researchers without PhDs - Simon Peyton Jones for example - so it can be done.