If you were synchronizing data to iCloud, you might be able to get that data back - as it would have been stored in iCloud, not just on your phone.
You can see what data was synchronized to iCloud by logging into https://www.icloud.com/ . If you saw, say, your photos there, you could get them back by re-connecting to iCloud Photos (same Apple ID), and giving the phone a chance to sync with iCloud. If the phone was not synchronizing data to iCloud before the catastrophe, turning on iCloud synchronization won't get your data back.
As far as anything that wasn't backed up, synchronized, or otherwise copied off of the phone – it's gone.