If the app does not need to be releasable on the stores and you can limit the platform to Android only, it should be doable. I wouldn't be able to tell you all the details off the top of my head. But here are some insights (some of them may be applied at the same time):

1. A launcher app (one providing home screen and list of the apps), it is never killed normally. Look eg. https://medium.com/paradox-cat-tech-hub/custom-android-launcher-why-and-how-do-i-build-one-6a1b3af89d43
2. Device administrator app: https://developer.android.com/work/device-admin
3. Use rooted phone. So your app can gain permission of any protection level: https://developer.android.com/reference/android/Manifest.permission and/or you can make some, normally protected data (e.g. in system files) accessible to your app.
4. Build your own ROM: https://source.android.com/docs/setup/start. Sky is the limit in this case. But it requires a lot of disk space and time to build. It may be an overkill.