Like others have mentioned, in my experience small startups can and do win Government contracts.

Most founders have intimate knowledge of the contract process and a large network from previously working at a large DoD contractor. Once they have this information and rolodex, they normally have an easy time running a small defense contracting firm as a sub on large contracts and winning their own through contract vehicles like SBIR.

This is also the story of how all those mega-mansions in Great Falls and McClean VA came to exist.