Can I restore permanently deleted photos

I sure hope not, as that would make the use of “permanent” here rather less than truthful.

That written... If the photos are not in the Recently Deleted folder, you’re left to look for a local backup prior to the deletion, and that’ll only work if you are not using iCloud, and if you do have a backup prior to the deletion, and if you are willing to revert all contents and all data on your iPhone to that of the backup. If the photos were in iCloud and have been deleted and are not in recently-deleted album, they’re gone.

Above assumes there’s no copy of the photos archived elsewhere.