You don’t need to get it set up with your domain. All you need is the IP address of the machine it’s running on; either local or Tailscale address. Just type it into the browser URL bar. I.e. 192.168.0.1:8080 is a valid URL.
Now, obviously you’d want to have the ability to do things like type a human readable domain name and have SSL certificates but they’re not technically necessary. Until I found the time to set up my reverse proxy, I used my Paperless using a bookmark to the IP address and port.
Pointing your domain at a Tailscale address is pretty simple, you just need to add an A record wherever your domain’s DNS zone is configured which points at the IP address (e.g. 100.107.42.69).