You can actually use, for example, any of the Raspberry Pi 3 base images on your Pi4. These will obviously run in 32bit mode rather than 64bit. My assumption is the base images you’ve tried to
apt-get install for the player don’t include it because the images they themselves are based upon do not. I’d imagine this is because omxplayer has not been packaged for
aarch64 (which is the 64bit architecture used by the Pi4). It’s probably worth just quickly testing with the Pi3 version of the same base image, to see if you can install/run it. If this is then missing in the relative Pi4 image sources, it would tend to support the theory. If you could let us know the base images you’re using, I could also check this for you.
At that point, it probably falls to either asking the maintainers of omxplayer to package it up for
aarch64, or compiling it yourself.