Google does not allow you to pick a default two-factor method.  Google sets what they consider the most secure method as the default.

The order they use is as follows:

1. Security key
2. Google Prompt
3. Authenticator app
4. Voice or text message
5. Backup codes

If you do not want to use that method, click Try another way.

You will then be presented with all the other options you may use.