I got a degree in mathematics, and didn't go the teaching route. after working for a while in the geophysics industry, I got bored and wanted more options- I realized the best way to open up a lot of options is to go the engineering route (every job posting I found interesting required a BS in ME)
so, go back to school. start at community college (get calculus, diff eq, physics, chemistry out of the way), and make a good impression on your professors there (evaluate the ones worth making an impression on). this isn't hard- you don't need kiss up to them, just volunteer to answer questions, sit up front, ask questions, etc. then go back to them and ask for letters of recommendation (masters programs usually require three)
then, (now this is key), get a 4.0 in your undergrad engineering classes (you'll need to take a few in order to 'catch up' to other grad students; but you won't have to waste time with classes outside of your specialty- I focused on thermofluids, and skipped advanced materials/vibrations stuff). Alternate between co-op semesters, and class/research semesters. Your degree will take a bit longer to complete, but you'll have a lot of fun, make important contacts, and have the chance to do really cool stuff (I joined formula SAE and EWB, and it was a blast)
After your first, or second semester, hit the job fairs. Try to get a coop/internship (maybe with an aerospace firm?). This will help finance your schooling- save your money, and use it for books/rent/food (not tuition, take out loans for that)
BUT this is assuming you want an MS in mechanical engineering. you say you want to go into STEM, and something space related. That's still incredibly vast- you could design fuel systems, airframes, engine components, heck (if you're good at it) you could make an entire career out of analyzing drag on nose cones!
So, don't say you want to go into space, quiet yet. Narrow down the field of STEM you want to work in- teaching math, researching biology, designing blu-ray players, investigating car crashes? I knew i wanted to go into ME, so I took the basic ME undergrad courses and fell in love with thermodynamics, and fluid mechanics- so I went the thermofluid route. I would've been happy designing pumps that move liquid chocolate around, but instead I get to work on the fuel system for the F-35
(also, read what color is your parachute)