Is there a way for you to get old messages back if you've never backed up your device on iPhone 6s?

Is there a way for you to get old messages back if you've never backed up your device on iPhone 6s? - 1

Nope

Impossible. Once the messages have been downloaded to the phone they are effectively deleted from the server.

Even if you live in a country where those messages must be stored for years by the phone company for scrutiny by national security services if required then they're stored in a form which is inaccessible to you and to the vast majority of phone company employees. In any case all that's often stored is the details of which number was called, where the call was from, where the recipient was, and the call duration.

It's up to you to protect that data by backing up your iPhone regularly, and Apple make that so easy that it can be an automatic process to iCloud and an automatic wireless process to your host computer and iTunes when you're near that computer. Sorry, but your failure = your loss.

No…

No backup, therefore no recovery.