You can install from a different repository of apps such as F-droid or any other FOSS repository. But that means you must trust the managers of that repository who are building the apps from source code with their own keys which means they have the opportunity to modify it in secret, maybe adding some module, and we wouldn't know. So we would have the same problem as we have with Google Play Store but now we shift the trust problem to this other repository's developers.
You can use another frontend to Play Store but we will have to trust Google, it just means we dont need a Google account. Also we need to trust Aurora store if we install with APK file because the devs could add some malicious module before building the apk file, so we won't know that by looking at the source code they have published. And if we install Aurora store from F-droid then we have to trust F-droid instead. So same trust problem no matter what.
We can also choose to just trust the developers of each app by installing the apps directly from the devs by downloading the APK file but then the trust problem is moved to each developer instead. We don't know if they are adding malicious code before building.
So no matter how we install apps, we will never know really, there's always a trust problem. Maybe the best thing to do is to isolate each app as much as possible. Create a different user profile for each app. And then decide on a case by case basis who is most trustworthy when it comes to which method of installing the app, but no matter what there will be a trust problem.
Or do i have something wrong or missing something?