So I read up that you can point to a Unifi controller that is outside your network.
I made mine visible, setup DNS name and port forwarded :8080 to it.
I think (but not sure) that you also need the STUN port open, I don’t have a note here of what the port is but I have for sure mentioned it in another post on this form. It might also be worth opening 8443 to see if the https traffic gets through so you know that your DNS and port forwarding is working, make sure you have a good password first and consider locking 8443 down to a specific IP / IP list to be on the safe side.