TBH, as someone who has been around people who programmed games, at least while I was in school, the common theme was that they did it as a hobby since they were kids.
I don't think its something most people are going to go into just by picking a major. A lot of times, these are the type of people who were at home programming their own games in their free time for fun.
So, introducing young kids to programming at a young age and maybe doing it through game development is the best place to start.
Personally I can program but the idea of programming a game doesn't interest me. Just not my jam.
. I've even had assignments where we had an option to program a game for a project and the other options were more practical programming assignments like building an alarm or something more everyday use and I would choose that or steer our group towards that. I think it takes a special interest in game development.