A future Android release might include the ability to manually backup app data to Google Drive, according to a correspondent for the Android development team on the Google Issue Tracker. The ability to manually backup data to Google Drive will include things like backing up app data, call history, device settings, and text messages.
Until then, if you’re stuck in a similar situation where your device doesn’t start a Google Drive backup for whatever reason, you’ll have to this ADB method highlighted by XDA. According to a report from the XDA on the matter, if you want to manually trigger the Google Drive backup, you’ll have to set up ADB on your computer and then enter the following command to start the backup process: