Almost every large business, including prime contractors, have an Approved/Preferred Vendor List, or something very similar, that lists the vendors and subcontractors that have been approved by the prime for quality, on-time delivery, and other factors.
Many small businesses work very hard to get on these lists. And you should, as well, because being on the list means that you have passed the test that allows you to sell your products or services to that particular prime.
How do you get on these lists? Basically, you need to do two things: First, you need to fill out their Approved/Preferred Vendor evaluation form, and second, submit to an inspection.