The way that I got into it was through Coursera first - I was a social studies teacher who wanted out of education after eight years. I took a couple free courses on Coursera through Penn State and found that it was something I really enjoyed. I continued taking GIS courses through Penn State until I got my Post-bacchalaureate certficate (which was either 4 or 5 courses), which I used to get an internship at a local government for the summer and then my first job. I'm not seeing the same courses I took, but UC Davis has a GIS specialization on there. Coursera was free when I took it and it charges now, but still less than any college would charge. You can try out a course on there and see if its something you'd really be interested in.
In addition, what I also did was find some companies very close to me that had GIS jobs available, and I sent their HR departments emails saying that I was interested in going in to GIS as an educational option, and wanted to see how it's used, and could I job shadow a GIS professional for a day just to see how it was used in a professional setting. They agreed and I just sat down and watched a guy work on a work on producing permit prints for a telecommunications project for a day while peppering him with questions. It was a pretty worthwhile experience - and I work in the telecom industry today.
Also, at least from what I've seen, knowledge and experience trumps education. A lot of people I work with either have associates degrees or a bachelor's degree in something else with a GIS minor. I haven't met anyone with a master's, and it doesn't sound like that on its own would open a lot of doors. Get your first job, learn as much as you can, and learn how to use Model Builder and how to code a little bit in Python. Having a little bit of coding experience or anything that helps you contribute to automation will make you more marketable. You can summarize GIS data and export into formats like Exel documents, and learning some of the slightly-more-complicated Microsoft Excel formulas will give you a leg up. A lot of management types are seemingly only management types because they know how Pivot Tables work. No exaggeration.
Another one in your first job is to keep an open line of communication with other departments that use your data - for me, that include field technicians, civil engineers, managers, and accountants. Learn some of their buzzwords, learn what they use the data for, and you can learn little tips and tricks to provide that information more quickly and you can make a little reputation for yourself.
Good luck, and welcome to the map nerd life.