Guys with "background" are a dime a dozen. It's always been the case, and it's even worse now. 80 bazillion guys with DD214s with a combat arms background.
There are so many variables to becoming an actual, no kiddin', make-a-living at it Firearms Instructor that it's analagous to saying "I want to be an astronaut." Most of us did many many other things before becoming an actual Instructor.
Like an earlier poster said, use your GI Bill for a legitimate degree.
Get involved with action shooting; there is a whole skillset that most military guys are missing, and you'll pick it up if you get into USPSA/IDPA.
Many shooting facilities expect some type of law enforcement background; I'm not saying that's fair or right........it just is. Get your degree, maybe get into law enforcement, take some classes, shoot some rounds, learn what you know, learn what you don't know, and meet some people in the industry.
None of the above is what you want to hear, and please don't take it personally.