You should not have been able to start a new game without creating a profile. A couple other people have reported this situation, though.
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin Enhanced Edition\PlayerProfiles\<ProfileName>\Savegames_patch' folder.
Check your My Documents folder, and see if there is anything there besides the new profile.
Try searching your hard drive for *.lsv files. Most likely creating the profile overwrote the folder being used, but maybe they were saved somewhere else.
I don't suppose you have a recent backup of your My Documents folder?
Do you have
Windows shadow copies enabled, if applicable? Try right clicking the PlayerProfiles folder, select Properties and (if available) switch to the Previous Versions tab to see if there are any previous copies.
You can try a file recovery program such as
Recuva, but it may not be able to completely restore a save, especially since the quick and auto saves are repeatedly overwritten. In general, the more you use the computer after files are deleted, the less likely they will be recoverable.
With the Steam version, if you had cloud saves enabled, you can check in the Steam install folder, as well as My Documents, since Steam keeps a copy of the profile and saves there, which it uses when syncing online. I haven't checked if Galaxy does something similar with the GOG version.
Steam has probably already synced, but (if applicable) you can try the program
Steam Cloud File Manager Lite (
download) to check or download online saves (or delete them). You need to be logged in to the Steam client and have the game's AppID (373420 for the EE).
