I used my savings to fund a 2-year sabbatical in which I wrote my own game engine using C++ and LUA (this was in the dark days of XNA, no Unity yet).
Towards the end of my sabbatical, I went to GDC and started getting involved in the scene and used my game engine to apply to AAA studios. I eventually landed a job in Vancouver BC and went to work at an amazing studio for the next 5 years, which gave me enough time to meet some co-conspirators and start my own studio.
After 5 years of hellish work, intense stress, and poverty wages, we created https://store.steampowered.com/app/656350/UnderMine/ which found enough success to make another game. It destroyed several relationships, burned me all the way out several times over, and caused me to tear my retina I was at the computer so much. It's hard to be honest with myself about what I would have done if the game had flopped.
So it's certainly possible to go from traditional tech into games. It can take a while. Everyone's path is different. Be prepared for some life-altering downsides to the games industry, especially on the indie side.