"Communication with the Mass Effect 2 server was interrupted or has timed out" error?

I am revisiting the Mass Effect trilogy as it's one of my favorite series of games. Having completed Mass Effect again I am trying to get Mass Effect 2 started but I never seem to be able to make a connection to the Cerberus Network, and as such I am unable to create a new game with the DLC enabled.

This occurs regardless of whether it's the initial connection to the Cerberus Network on game startup, or attempting to (re)connect to the Cerberus Network from the menu option once you've got to the main menu. In both instances the game will sit on a screen stating it's trying to connect for ~30 seconds before timing out with the message "Communication with the Mass Effect 2 server was interrupted or has timed out".

I have tried installing the game both via Steam (with DLC installed manually), via Origin (with DLC installed automatically), clearing Origin caches, verifying the game files in both Origin and Steam, setting up firewall rules, completely disabling the firewall, running the game as Administrator, connecting directly to the internet with no NAT, and basically everything else I've come across while searching for an answer to the issue but still the same connection failure.

Mass Effect 2 is also not on EA's list of games with withdrawn services so I would expect to be able to still run the game without using unofficial solutions.

How can I get Mass Effect 2 to connect to the Cerberus Network?