Lateraling to a bigger IB -- coming from small MM bank

Hi everyone, 

I want to go into PE, but I'm at a 70 person/lesser-known middle market investment bank, so I don't think I will get much love from head hunters. Therefore, I think my best bet is to stick it out for 3 years in IB - 1 year at my current firm, then lateral to a bigger bank that headhunters recruit from for 2 years - to increase my odds of success for getting recruited. 

My questions are as follows: 

1. How do I successfully lateral to a bigger bank? What does this process look like? 

2. Am I correct in saying that it will be highly unlikely that I can recruit PE directly out my small MM investment bank? If not, how can I get in front of headhunters since they're not reaching out to me? 

Thank you for your time!