Google appear to be intentionally hiding the option to use an authenticator app such as Google Authenticator, 1Password and LastPass to store and generate 2FA codes for your Google Account login.
You can use them, but it’s not clear how, and you have to temporarily submit a mobile number you have access to before you’ll find the option available to you.
- Head to manage your account.
- Choose to add 2FA
- Select to do it via SMS
- Submit your number
- Enter the code they send you
- On the next screen select to add an authenticator app
- Follow the steps and submit the code you can now access
- View the backup codes and store them somewhere safely
- Finally you can remove your mobile number from the list of option
So to not use your mobile number and SMS (which is vulnerable to hijacking) you first have to submit your mobile number ¯\_(ツ)_/¯