If you have a central matchmaking server you can do NAT punchthrough to circumvent the need to do port forwarding.

Though its not 100% guaranteed to work so in some cases it might be necessary to route traffic through the central server, or do port forwarding manually, so take that into consideration. You can probably find statistics online for how well it works.

You also need that central server to recieve the "IM HERE" data to then log that IP to have the two sides be ready to link up (one calls for a connection to the 'random' other, is given the ID, then attempts one connection at time). Some state sequencing is needed because one would be the caller and the other a receiver. The NAT issues then need to be resolved. Im not sure of the details of direct peer-to-peer after the initial steps through to the central server(s)