Data which is NOT backed up can't be moved at all. You suggest you think you didn't backup. If you didn't, there would be no way to move data which stored anywhere to your new phone.
When you get your new phone, during the setup process, it will ask you if you want to set it up from backup if a backup exists. This means you would sign into the new using the Apple Account and Password used on the now stolen phone. If you are not offered the option to restore it from backup, then no backup exists.
That still doesn't mean your photos and some data weren't synced with iCloud. So sign into the new phone with Apple Account and Password. Open Settings > Tap your name at the top > Tap iCloud > turn on the switch for all apps which could sync with iCloud. Any data which was synced with iCloud, will them be moved to your new phone. If no data was synced with iCloud, then you're out of luck completely.
Backing up your iPhone using iCloud is simple and doesn't actually require you do anything other than to turn on the switch to backup when the phone is locked, plugged in to charge and connected to Wifi. If you've lost all of your data, this will be an unfortunate lesson you can avoid going forward.