I'd suggest not applying until you are competitive, although some say they take notice from persistence. I attended a job fair first, handed in a resume, then applied. Took about two months before I got a phone call for interview. The biggest issue now for people is that they are competing with pilots from other ACMI's making lateral moves already typed on 747, 767 with lots of international experience.
It's always a numbers game. As a relatively inexperienced pilot, and I mean this as some one with no heavy time, Boeing/Airbus type, international experience, used to the kind of schedule/flying we do, your chance for a quick, down to earth freight dog interview was under the old contract when people wouldn't even show up to the interview. You now need to treat this process the same as if you were applying to the big five.