How to escape LMM IB

A1 at a LMM bank - relatively though not completely unknown, (i.e. people have lateraled banks and gone to MM PE from here). Deal volume and reps are actually pretty solid. I’ve been fortunate to have been staffed with some of the stronger seniors at the firm and hence should have some real experience to speak to, but the types of clients we work with / pay / exit ops are not ideal so still would like to jump. Went to a strong semi-target and otherwise have a decent resume, but just didn’t recruit as well as I could’ve as a sophomore so here we are.

Any tips on overcoming brand in lateraling and when’s the earliest you can do this? Is it worth reaching out to IB lateral headhunters at some point? When should I think about reaching out to alumni / cold applying? Thanks