At the beginning of the game your character help Big Boss leaving the Mother Base, but soon after that a wormhole appears over the base. Somehow your character manage to save himself from being sucked into the wormhole, but he loses an arm in the process. Apparently he got infected too, and he dies right after. Somehow Goodluck, a new character, during an inspection notices you resurrected, with your arm growing back. You are still infected, but you can't live in this worl anymore, so Goodluck sends you in a mission inside the wormhole to retrieve Kuban energy, an energy which should resolve all the conflicts around the lack of resources in our world. So your character go in this parallel world, he starts on doing stuff to retrieve the energy, he rescues some characters in the middle. But there's something going on, because apparently the previous squad sent in the mission was wiped out. So while they do the stuff to retrieve energy and find a way home, they rescue a child too on a wheelchair. You find a way to go home, you open a portal but instead this lure the Lord of Dust, apparently the chief of all infected near your base. You manage to escape and leave into the wormhole, just to be teleported in a different location, your fob. This is the second part of the game, where your character discovers there's another survivor, who apparently killed the previous squad members you discovered being dead. You meet him at the same moment he is trying to kill a dude you saved in the intro of the game. You save him and he go back to your Fob. You do other stuff to find a way home, and in the middle you discover Sehelantropus. You also discover that the dude you saved is infected too, and the dude who was trying to kill him already knew that, and he is the sole survivor of the other squad. Your squad receive a message from Goodluck, apparently the general who instructed you to increase the power of the extractor during the first wormhole opening just wanted to lure the Lord of the Dust, so he got sucked into the wormhole too. You need to open a new wormhole to go back home, but you also need to kill the Lord of the Dusk, and the only way to do so it's recovering the Sehelantropus and its railgun.
You also discover the world you ended in is not a parallel dimension, but it's our world, far in the future, turned that way by nanomachines. So you recover the Sehelantropus and you need to go back to Code Talker's home in order to retrieve some data to build a trap of Archaea Metallica. You recover those, you build the trap, you lure the Lord of Dust and send back home the child you rescued before. Turns out the child instead is Goodluck, who ended in Philadelfia, 1943, instead of our days. Eventually when he became an adult, he orchestrated the whole thing, sending you back in time, to kill the Lord of Dust. You and your squad decided to not leave the world via the wormhole, and stay to kill the Lord of Dust and eventually save the normal time-line.
You do this, killing the monster with the railgun, but the monster couldn't properly die until one of the AI sacrificed itself (so goodbye to your opportunity to go back home) to teach the monster how to die, since it can't understand the concept of death, since it was formed by nanomachines. So the pod go inside the monster, the monster dies and turns out the pod was built with anti-nuclear material so it survived. There's still a possibility to go back home and now, with the lord of dust gone, you are not infected anymore. Game over.
No Big Boss in the game if not in the very first cutscene, no Quiet, and not any references to other characters happen in Survive.