What to do if I can’t log into my iCloud for Find My iPhone?

Two factor authentication can only be enabled two ways. First is by the Apple ID owner through Settings. Second a brand new Apple ID has it automatically enabled which has been standard for considerable amount of time now.

As for tracking and marking a phone missing or lost, it does not require two factor authentication. Apple has a support article that gives you step-by-step instructions and options. Find your lost iPhone or iPad - Apple Support :

Use Find Devices on iCloud.com/find

When you sign in to iCloud.com/find, you don't need to enter a verification code — so you can use Find Devices even if your trusted device is lost. If you're asked to enter a verification code, select the Find Devices button instead. On iCloud.com/find, you can also mark your device as lost.

Read these support articles to find out how to use the Find My app to locate a missing device or item. Click here --> Find your lost iPhone or iPad - Apple Support and Use Find My to locate your lost Apple device or AirTag - Apple Support

- A person can use the Find My app on a device owned by someone in their Family Sharing group.

- Alternatively, anybody can sign into https://www.icloud.com/find to locate their device using a browser. You don't need a two-factor code if you use any internet browser and log into www.icloud.com/find

Note that the address must include the "/find" as shown above.

Read this support article about what to do if a iPhone or iPad is lost or stolen -->

Find your lost iPhone or iPad - Apple Support