The phrase "to make an omelette" means to create or accomplish something by going through a process or facing certain challenges, even if it involves breaking or sacrificing other things in the process. Full definition
Also «you can't make an omelette without breaking some eggs» is a really nasty way to talk about, say, crucifixions. (nakedpastor.com)
He does not try to say that after all his secular service is willed by God even if it involves apparent worship of Rimmon — one can not make omelettes without breaking eggs, it is impossible not to have dirty hands. (religion-online.org)
As it turns out, I was talking about making omelettes with some coworkers, and at a table of four of us, two people said they made theirs with flour. (jenncuisine.com)