Startups can and do get government contracts, but the government isn't going to come court you. You (the startup) have to figure it out yourself. Selling to the government is very similar to selling to any other industry/company: you (the seller or maker) have to understand the customer's acquisition process. The big difference is that the federal government is the largest customer--millions of people and trillions o…
Startups are fast, but they aren't always reliable. At least for values of reliable that == being able to throw money at {Large_Technology_Contractor} to have them parachute in an additional team of engineers to solve unexpected problem X. Or being around 10 years from now for support.
But agreed, there are all levels of involvement. Consider the prime contractor's cut off the top the price of getting bid into the game and contact with the right people, then do your best to work your way up!