How to navigate PE recruitment when trying to lateral from a MMIB to BB/EB?

I am currently a senior and will be starting at a lower-tier MM IB as a generalist that primarily focuses on capital raises but also has M&A capabilities. My goal is to eventually transition to a tech PE MM-UM-MF buyout shop. However, I understand that I may need to lateral to a BB/EB first. My question is, when should I start preparing for PE recruitment? Also, if I am unable to lateral to a BB/EB, should I consider pursuing LMM PE instead? I'd appreciate any help. I am a non-target, non-diverse candidate, and unfortunately, I don't have anyone in real life I can ask. I've been on WSO trying to gather as much information as possible, but I feel somewhat lost in the situation I am in.