Can Full Cone NAT router automatically opens dynamic ports to Symmetric NAT router?

Question

There’s a software that provides peer-to-peer connections using random private dynamic ports in such way that the software will get users Public IP addresses and port information and store its specific unique source IP and port for each user’s Public IP address.

For example: in order for a source IP to connect to destination IP, it will retrieve that information from the software servers that has already stored IP/port of destination information of let’s say IP: 111.222.333.444, port:56344, and then initiates that connection with destination IP successfully which should work most of the time in this case.

To make things more complicated, let’s say the user router’s NAT Type is set to Symmetric NAT which in this case the user network information will be stored in software as a predefined source IP/port but due to the nature of how Symmetric NAT works, it is NOT going to be the same initiated source IP/port when creating a connection session with destination IP because it is going to use different source IP & port altogether and that contradicts with software servers conserved predefined source IP/port that was saved beforehand, thus joining session will simply fail.

In theory, a user that has Full Cone NAT router should be able to communicate to a user that has Symmetric NAT router because it will allow any incoming connection for any source/destination port.

With all that said and explained, it is worth mentioning that the software recommends opening port 3074 for it to work properly. The question is: if this specific port doesn’t work for Symmetric NAT users (that did not port forward), then why it is advised by the software in the first place?