Game dev is extremely hard to break into. I've been in and out of the industry for some time now.

If you're dead set on working in the industry I'd strongly advise going the platform integrations route.

1. Gain experince working with API services and creating some C++/C# integration wrappers for UE and Unity (GoDot potentially too).
2. Pick up some contract work doing API development outside the games industry to strengthen your knowledge and experince developing solutions.
3. Find a game team that needs a platform(s) integration engineering role or a central publishing engineering role.
4. Develop a host of solutions professionally for a year or two.
5. Make the jump into the role you actually want.

This also gives you a ton of job flexibility in an industry that values knowledge breadth and has waves of job stability. Automation & tooling engineering, API development, services engineering, etc.