And adds 20ms+ latency, another complex point of failure, and potential problems depending on the reputation of the IP address block of wherever you're hosting the endpoint. I've used VPNs to smooth over various Starlink problems since I got the service and it helps but it's not a great solution.
Most likely you wouldn't with CGNAT, unfortunately, at least I can't see how. They need to ping your IPv4 address to set up.
As an aside, they also want to ping your IPv6 daily (at least in my logs) to keep the tunnel alive; otherwise quite stable.
I'm fortunate to not have to deal with CGNAT. But still waiting for IPv6. A he.net tunnel works for now for what I need: stable IPv6 for SSH tunneling from my IPv6 mobile.