Is there any way to recover photos or videos from years ago if they’re not backed up?

If you at some point turned on iCloud Photos they could be out there in your account, log into your iCloud account and check. If not then there is no place to recover them from.

Where would you be recovering them from if you don't have backups?

Johnathan’s reply was designed to encourage you to think about the retrieval source - if you don’t have a place to retrieve something FROM then retrieval cannot happen.