Do you mean without running discourse-setup or do you mean without building the container that is required to run Discourse? If you mean the latter, it’s possible by pushing the old image to a repo that the new server could use, but that’s not something that a novice could easily handle.
Your process was complicated by the PG13 upgrade. It might have been a bit easier to build a new image from scratch on the new server and backup/restore the backup from the old one, but you’d still have some fiddly bits on getting the new server to get the let’s encrypt certs.