Sure, it's not convenient for normies but you can just download the apk from somewhere and then install it, just like you can do with an .exe or installer on windows.
You can use Fdroid and sideload apps, but Google makes it impossible to run most apps without Google Play Services running in the background.
> but Google makes it impossible to run most apps without Google Play Services running in the background.
It's actually the developers of the app doing that. I make sure to minimize such dependencies.