Help first, ask later - that's how mentorship begins

Go reach out to a PM and ask how you can make their day easier. Figure out what you can do in your spare time that they can offload to you and do a little bit of volunteer labor, even if that's just shadowing because I think just getting that context and understanding the sort of rhythm of how a team ideates and defines problems and prioritizes and ship software is the experience that's going to be the most important.

Don't ask a person to be your mentor. That's really awkward. First, identify them. Say, this is a person I think that could be helpful to me. And then, find ways to be helpful.

Once I have this outcome, I work backwards to figure out how am I going to do that. What I do then is I start asking questions and then I find the best people in the field and I just go talk to them.

Don't feel ashamed to reach out to something for help. It gives a lot of them great honor. The biggest honor most people get in their lives, or one of the biggest honor is when other people ask them for help. Because we all just want to feel useful.