How do I recover data from a stolen iPhone without security questions?

You cannot recover data from a device unless you were syncing to iCloud or have a backup on a computer. See How to use account recovery when you can’t reset your Apple Account password - Apple Support

You cannot get data back from a stolen phone that has not been in your possession for 7+ years.

As for getting data that was synchronized or backed up to iCloud, you will need your Apple Account credentials.