PE Recruiting Timeline with HH

Incoming first year and have had a handful of HH reach out for introductory calls last few weeks. I don’t plan on doing on cycle as I think MM PE is where I’d prefer to be and just recruit off cycle. In the outreach emails they all say the same thing about how it’d be great to connect before it picks up, but I’m wondering if I should be having intro calls if I’m not going to do on cycle?

Will I be at a disadvantage for off cycle opportunities if I talk to HH too early and they in a way forget about me?

Could use some insight. Thanks.