This can be a very difficult market, but there are a handful of different projects designed to help with this. In-Q-Tel [0] has been accelerating adoption of new technology for the Intelligence Community for many years and often invests in and helps deploy technology from startups of many sizes. SBIRs [1] can be an effective way to quickly get gov money for research and even culminate in a procurement vehicle for sole source contracts if you get through Phase III. There are also a handful of accelerators like DIU [2] and MD5 [3] designed to help small firms navigate this difficult space. It still isn't easy, but it can help level the playing field a bit when you are just a startup.
[0]: https://www.iqt.org/
[2]: https://www.diu.mil/