Ab-Initio Training
The big airlines don't need to run abinitio. They can simply pick up the people wanting to move on from low cost carriers.
I suggest you broaden your horizons much wider than that paltry handful you suggested there, and I hate to burst your bubble but if you go to an interview and tell them that you've just been waiting years for a chance instead of actively developing yourself, they'll probably set fire to your application in front if you.