I've heard that you can configure your Google account to use its (more secure) authenticator app rather than sending you a text message - in my most recent case, this was when Google sent me a text message to "make sure it was really me" when I signed in from an unknown device.
However I can't seem to find any setting that allows me to switch Google's mechanism of 2FA to the authenticator app for this scenario. Is it possible or will they always use the text message method?