Deleted profile that wasn't backup will not recovery since it is gone now. Sync isn't a backup method it only syncs between devices and any original data from the PC that was uninstalled or delete will be removed from the other devices since there is no data to sync back to now. What you should've done first was follow Firefox FAQ on how to backup the bookmark, profile and data before uninstalling Firefox but once that was done all the data was gone. So there isn't any data to restore back to since it's gone now.