Ooh, that update about tuition assistance is helpful - thanks for that @Sportsman88.
OP, I’m not sure that the best way to NASA is joining the Navy, furthering your education and getting research experience. It is one way to get there, though. NASA scientists and engineers very often have a military background, particularly because veterans get preference in federal government hiring.
As for NASA - where do you see on the website that you need to have at minimum a STEM-based bachelor’s?
I see this page (http://nasajobs.nasa.gov/jobs/occupations.htm) where it does indicate that 60% of NASA’s workforce is professional, scientific, and engineering. That makes sense because NASA does space exploration and investigation, so majoring in a STEM field (or acquiring an MS or PhD in it) is probably a good way to get to NASA. But the other 40% is clerical, administrative, and managerial - things like human resources, budgeting and financial, public affairs, etc. NASA is an organization like any other; somebody’s gotta do payroll.
Are you talking about the astronaut program? Because that’s a whole different kettle of fish.
NASA jobs are advertised on USAJOBS.gov, just like other federal jobs. A quick search shows they are looking for different kinds of positions. There are engineering technicians, research materials engineers, software developers, astrophysicists, environmental protection specialists, physicians, and nurse anesthetists. But there’s also an ad for a human resources assistant and one for investigative counsel. (However, note that there’s just one of each of those, while there are several for engineers.)
Either way, though, that’s a moot point. If a requirement is that you need to have at minimum a STEM bachelor’s degree and you have a PhD in a STEM field, you have exceeded the minimum.