Recover Files in iCloud
Yes, you're in luck — this is in fact possible!

Login to iCloud, and then click your name in the top right of the page, and then click "iCloud Settings." Scroll to the bottom of the page, and in the bottom left hand corner you should see an "Advanced" box:



Then, click "Restore Files," and it will take you to this window:



If your files are not in this window, then I'm afraid you're out of luck!