The source would need to return a new image each time the URL was accessed.
As far as I’m aware, Google Photos doesn’t have a native feature that would return a random image from an album each time a special URL was accessed.
If you figure out a solution, be sure to post it as I’m sure other community members would be interested! There’s also a feature request for native Google Photos integration if you want to cast a vote on that and perhaps reply with your use-case to help ‘bump’ the thread?