If I were in your position (looking for work in aerospace) I would:
1. List every company that supplies ___(space flight systems, etc.)
2. Research recent contract awards to those companies. I don't know how to do this, but I'm sure it is public knowledge. When a company gets a contract to produce something they need new warm bodies to do all the work.
3. Get into direct contact with those companies and ask for an interview...they always are ready to take recent graduates for junior positions. You have to start somewhere. Once on board you can prove your competence and they will value you (with salary increases, paid training, tuition aid towards your Master's, and more benefits).
Unrelated example: When Boeing won the contract for approximately 30 new "Dreamliners" last year they hired more than 1,000 newbies.