You can set up two-factor authentication using a mobile app instead of using Google or simply an email+password login.
NOTE: If you signed up with Google or similar this authentication method will be disabled.
You begin the setup in the profile menu.
Clicking Setup using a mobile app will generate a key you can add to your authentication app.
Once you have your response key from the authentication app, enter it in the Verify step and click Enable two-factor authentication.
You will notice that the two-factor authentication section changes and instead there is a link to view recovery codes.
Please make sure to store a copy of these codes in a secure location.