I am in the same boat. Like I don't work for NASA but the rest is pretty much the same.
So no experienced advice here, sharing my thought process: my intent is to complete a private license, and then go for commercial/instrument/Flight instructor ratings.
This will take time for sure, but I am not planning on quitting my job right away. Not sure if I'll be able to get a part time flight instructor gig (week-ends) while I work full time during week days, but that's kind of what I hope for and in the mean time my full time job will help me pay for my own recreational flight hours over