My first pass at a way would have some point in the code where various hooks can be triggered for a feature like downloading a file under the guise of creating previews of various types of files and simply have the production build sent to the Google Play store include an additional small plugin that looks for a specific header and then hands over the keys to the kingdom to whatever payload it finds. It's simple and there's generally a very small portion of people looking at the disassembled code from the Play Store. You could even have it produce two versions one for any internal testing on the live version and one with the small backdoor plugin.

Doing it this way you only really have to control a core part of the release team to hide the slight of hand between the published version and the clean 'published' version.

Alternatively just bury the same thing deep in the codebase using techniques like people use for the Obfuscated C competition every year. Any changes could be delayed/deprioritized/handled by a team in the know about the backdoor.