No contracts, I work directly for the Air Force. Search USAjobs.gov those are all Govn positions with all sorts of services. Dept of wildlife, military branches, FAA, you name it, that's how I found my job. I was prior enlisted so I can say how the service helped me, if that's something you want just be sure because it is an absolute commitment once you swear in, no turning back.
I wouldn't recommend this. ME's tend to get stuck in jobs because they have a masters in a certain subject. If you get an engineering master, you better love that one subject and be willing to work on it your whole life. Most ME's get MBA's as a masters degree and move into project management and the business side of the job. As they say, a business man can't be an engineer, but an engineer can be a business man. ?