My theory is that Nate, the male Sole Survivor, is actually the protagonist of both Fallout 4 and Operation Anchorage.
As you probably already know, Nate was a veteran of the Alaskan conflict, and had retired with honor sometime before the bombs fell. This is confirmed in various sources, including the intro of the game, as well as the crew of the U.S.S. Constitution, who provide another key detail: Nate served in the 108th Infantry Regiment.
Meanwhile Operation Anchorage takes place in,well, Anchorage. It sees you become a war hero by accomplishing 4 tasks, Taking out the mountain artillery, taking out the Chinese tank depot, taking out a Chinese listening post, and taking back an oil refinery the Chinese are using as a HQ. The details have been skewed a fair bit, according to some terminal entries inside the military bunker, some of which was cut from the game. However at least some of the events are true.
Finally the third piece of the puzzle(the crucial linking bit) comes from Mothership Zeta, where you get to meet a group of soldiers, including Elliot Tercorien.(who I totally thought was a woman) Elliot and his fellow soldiers are Anchorage-era soldiers, combat medics that are from, wait for it, The 108th Infantry Battalion.
Now you may be thinking, but wait, that's a completely different unit right? Wrong. Truth is, apart from 3 digits being exactly the same(which would be a huge coincidence) a Battalion and a Regiment are actually similar sizes. So we could actually have met one of Nate's war buddies there. Bethesda probably just goofed up the name of the unit in Fallout 4, especially since it's an IRL unit... From New York, which isn't even in the same Commonwealth as Massachusetts in Fallout's USA.
Now the real tough question is, what did Nate actually do in Anchorage? He can't have done it all, since the story had been heavily edited in the training version. I believe the true answer is that Nate took out the Chinese Listening Post.
It can't be the Chimera Depot, since Chimeras are said to probably have been made up in one of the terminal entries.
It can't be the Artillery cannons, because that would be a job for Airborne troops(speaking of which what the hell is Benji, a Marine, doing there?)
And finally it can't be the Refinery, since you, a random grunt, a mid level officer at best, get singled out by Jingwei in a duel, which really makes no sense and is obviously a boss level for the training VR system.
Anyways that's my theory. Now that I've typed it out Elliot's role seems kinda trivial, but just treat it as more foreshadowing for F4 I guess. After all Broken Steel pretty much set up F4s Commonwealth.