That you could do, is adjust the date of the photo you want to use as the cover. Since the sorting is done by date - it will always be last.
A great work-around. That will work, but only on the two most recent system versions, where the date will not be stripped. And the drawback will be, that we no longer will share the photos with the date they have been taken The subscribers may not like it. We will have to change the date of the photo in our library, before we share the photo, so we will be losing the date as well. I recommend to do this for a copy of the photo, not the only version we have. And to share the photo with the original date as well.
It is only recently, since iOS 16/iPadOS 16, macOS 12 Monterey, that the capture date is no longer stripped, when we are sharing an album and the items in the Shared album can be sorted by the date at all. It would be a pity to sacrifice this first improvement to shared albums since they have been introduced in 2012 with OS X 10.8 Mountain Lion. We had to wait a very long time to be able to share our photos in Shared albums with the date they have been taken. The locations, titles, and descriptions are still stripped.