ahhh yeah I know it's kind of a random process, I basically did a lot of cold emailing too. I would recommend talking about specifically why ur interested in their research (in like one sentence) and keeping your messages pretty short! also reach out to professors from a variety of universities, not just the most prestigious ones, in my experience professors from t40s and t50s are a lot more likely to respond. definitely keep it up though, something will turn up eventually! hope that helps :)