At that point I'd just point out how coming up with an estimate would first require putting in a lot of exploration and research, so it would take X amount of t

At that point I'd just point out how coming up with an estimate would first require putting in a lot of exploration and research, so it would take X amount of times and obviously delay other work in the meantime. Then ask again if, that being the case, the manager still wants their estimate. Now it's on them to do their job and evaluate priorities instead of sneakily offloading this to the developer.