path to PE: small IB->BB/EB->PE or small PE->lateral PE?

hi all, I'm one year out of undergrad and I'm trying to eventually pivot to PE from my current field, which is completely a irrelevant/non-finance field. So, if my eventual goal is a big or UMM PE, should I try to find some unknown/random 1-10 people IB shop to do an off-cycle internship or 1 year analyst, then try to lateral to an EB or BB, then to PE? Or, can I try to find something at a 1-10 people PE, then lateral to a bigger PE shop?

Key considerations here: 1. how is a 1-10 people IB regarded? Is it possible at all to get to PE from such an IB? What are the chances of actually laterally getting to BB or EB? 2. it seems that some PE shops do hire analyst-level directly out of undergrad (and not just super small PE, but bigger one like the riverside company, ares management, etc. that have structured SA PE programs and analyst classes). So, maybe I can lateral to these firms from a small PE and skip IB altogether? 3. If I skip IB altogether, would that impact my chances of ever getting to a UMM PE or bigger? Will I be stuck in tier-2 PE shops forever or need an MBA to achieve that?

Maybe there's something else I haven't considered, if so, please point that out. Thanks!