By using the Asset resource from the Admin API.
Enable your app manually, click save, then go and Edit Code from the theme editor and look for config/settings_data.json.
You will find a block related to your app.
Obviously the step above is just to learn what the whole deep link method and manually switching the thing on, which is the "normal" process is, really does, and you do not need to do this after you have the json block you need for the next step, which is really how to automatically turn your app on when installed.
Now use the Asset API to GET the key=config/settings_data.json add in the same things you found when you looked at the code, but put "disabled" to false.
PUT that back into the API, and the App is turned on 😉
While I did run this in production and it does work, be very mindful that there may be other plugins or things mixed in as well, so you will have to make sure you do not overwrite anything when pushing in the additional block.
