If you didn't have a backup to iCloud or to a computer, the other thing to look for is to see if you had any data synced with iCloud. Use an internet browser and log into www.icloud.com and see what is there. The data that you can view there (if any) is synced and can be synced with a replacement phone or other Apple device by turning the same sync options on. For example, for photos see: Set up and use iCloud Photos - Apple Support
or for Contacts, see: Set up iCloud for Contacts on all your devices - Apple Support
If you didn't have any data backed up and didn't have any data synced, there isn't another option.