Expose a Computer
There's a way around port mapping, whether automatic or manual, for a single computer: you can expose the machine entirely with a feature called default host or DMZ, to offer just two of the many names this feature has.
Using this feature, a host—a computer hosting services—with a private network address has all its ports mapped to the same ports on the router without any manual configuration or assignment. Every port has a one-to-one relationship from the router to the computer.
The feature is enabled slightly differently on every router, but you essentially first choose a particular computer's IP address—whether you assign that address manually to a computer or through DHCP reservation as described earlier in Assign a Fixed Address ...