I've never cold connected to anyone. I wouldn't know how to go about doing it. My first idea is to find members of teams that cited one of my papers, but that makes me sound neurotic about papers, doesn't it. I've had the application page for OpenAI's position open for a couple weeks now, I'll give it a serious try tomorrow, and see if there's any team member that at least 2 degrees of separation from me.
Find them on LinkedIn and ask to grab a cup of coffee or jump on a Zoom. Be open about the fact that you're interested in what makes a good member of the team. Ask about what you can be upskilling on. Be friendly.
Also doesn't hurt to reach out to potential managers as they'll be able to provide more direct feedback.