Most VPNs use UDP. So set up a wireguard, tailscale or openvpn.
But you still need to “open up the firewall”. UDP still works on ports the same way as TCP. I do agree however, that exposing a VPN port is more secure than exposing a port for a game server, as you don’t know about the security of that server software.
If you want any system to connect to you, you need to open a port. You don’t need to do that for outgoing connections (the OS and your router will automatically open ports for the return connection). So if everybody connects to one central system, nobody needs to (explicitly) open any ports (except for the central connection point)