Networking for PE exit (2021 grad)

Hey everyone.

Soon will be graduating from a decent school and going to MM IB. Recently met a few alums at a MM PE I'm really interested in. They work somewhat frequently with my bank and seem like good people. The PE firm sounds like a relatively competitive shop, and I'm wondering what route I should take for networking there. I've already done some basics reaching out via email, linkedin, etc. and I'm planning to meet up with some of them when I start FT.

Should I...

1. Play it cool and stay in touch until I have more work experience under my belt

2. Go hard and keep my name fresh in their minds for the next 1-2 years before I would be exiting to PE

Mostly just curious if spending time communicating with them now would lead to a payoff in 1-2 years, or if there is no point in bothering them much more than an occasional email until there is more serious recruiting.