The idea here suggests uploading to F-Droid, but this has been blocked for years due to having to build with Qt.

Accrescent is an open-source app store that is gaining traction, as an alternative to the Google Play store, without sacrificing security or privacy.

Details on how to submit to the store can be found here:

Essentially, the QField team would have to sign up to the Accrescent developer console and verify themselves. Then the signed APK would have to be uploaded manually on each new release to push through updates to users.