LMM/MM SA -> UMM/EB/BB FT?

Hi monkeys. I accepted an offer at a LMM/MM for SA 2022 and am looking to make a move asap. I understand that conventionally, I would do the SA gig, get the return offer, work for ~1 year, and then lateral. But if I'm aiming to move to a different bank (UMM, EB, BB) for FT, then how early should I start networking? As early as SA 2023 would? Also, if I were to start networking for a different FT bank before I even started my SA, would this be looked down upon? And if I do so, is it okay for me to put incoming IB summer analyst @ LMM/MM on my resume to make me at least somewhat more competitive among FT candidates at the better shops? In any case, if I do try to make this kind of move, I would have to have the UMM/EB/BB offer in hand before I need to make a decision on a potential return offer from LMM/MM, correct? Or is reneging from LMM/MM for UMM/EB/BB not that big of a deal? Would really appreciate any insight into these questions. Thank you very much.

P.S. Found this website about half a year ago, and it has been a tremendously helpful resource to me as a junior in college. Hence, thought I would reach out to the community for advice in regard to a specific situation I find myself in. Thanks again.