Is it possible to recover permanently deleted photos and videos from iCloud?

When you say "permanently deleted," I assume that you mean that you deleted your photos and videos from the Recently Deleted album as well as from the main library. That Recently Deleted album is your safety net, and by deleting photos from there, you cut it.

It's too late to back up the copies in the iCloud Photos system. Permanently deleted means just that.

If your Mac was participating in iCloud Photos, and you were making regular backups of your Mac, you might be able to get back some photos and videos from your Mac's backups. Say, from a Time Machine backup, or from another kind of backup made before you did the deletion.

Permanent means just that, PERMANENT. Once permanently deleted, there is no way to backup what no longer exists.