Listen, always apply. I don't turn 23 until July 2014 and I currently am in my 2nd year at a 121 airline.. True, many denied me like Eagle, Skywest, XJT/ASA, Lakes, but 2 121 carriers gave me jobs.
I work under one of the most favorable regional ALPA contracts. When I thought I had missed the deadline and would be stuck flying corporate, I made my way in.
It's not impossible, just get ahold of people. I had a training dept guy at ASA get my stuff to Baxter. Unfortunately they were stuck on the 21 year old deal then as well..