If you have only one communication device, and no other internet access (no computer, no landline, no family, friend or neighbor with a computer, cell phone or landline) then you had better never lose your iPhone, because if you do your Apple ID account will become inaccessible. Of course, if this is your situation you won’t need to access your Apple ID account, anyway, so the fact that it is inaccessible is irrelevant.
But as long as you have your iPhone you can use it as your only a means of entering an authentication code. Of course, except for the first time you will never be asked for it again.
But you can still enabled 2 factor authentication (you actually have to when you created your Apple ID).
In the article you referenced that you said didn’t help, I found:
- On your iPhone, iPad, or iPod touch: Go to Settings > your name > Password & Security. Tap Turn On Two-Factor Authentication. Then tap Continue and follow the onscreen instructions.