As long as you don’t close the game, your changes don’t get synchronized to Steam Cloud. So you can head to your local Steam Cloud folder and copy the savegame from there.

Windows: C:\Programme (x86)\Steam\userdata
macOS: ~/Library/Application Support/Steam/userdata
Linux: ~/.local/share/Steam/userdata

In that folder the BG3 saves will be under Your_User_ID/1086940

Or you can download your savegame from here: https://store.steampowered.com/account/remotestorage

If you did close the game though, Steam Cloud won’t have your savegames anymore either and even the Steam Support won’t be able to restore them.

Also take this as your sign to start making regular backups of your files ;)