If it is saved in the cloud, they should be accessible in some way. That should mean they are saved on another spot besides your computer, whether it was via an account (Which you would just need your account name and pass) or another method.

I don't save mine via the cloud, or I'd probably be able to help you better on getting them back.

1. Start GOG Galaxy.
2. Find the game, then click Extras in the category selection at the top.
3. Click the file listed in the Cloud Saves Backup section at the bottom. If there's no save data on the server, the Downloads category will show a failed download with size - / - MB.
4. Manually extract the archive into the save folder.
5. You can also start the game via GOG Galaxy, which will hopefully sync your saves (i.e. automatically download and place the saves where they need to go). Don't do this without downloading the backup first, in case something goes wrong.

There's no way to download your synced saves without GOG Galaxy.

It doesn’t help you now, but I always recommend backing up everything offline. It’s always under your control then, you can have as many as you want, chop and change, and not be locked out. If you need software to do it for you there is:
https://www.gamesave-manager.com/
But really, it’s not difficult to do yourself and far more powerful and controllable than galaxy.