...the future version of The Kid?
At some point near the end of game The Narrator says something along the lines of, "Did I ever tell you about when I was the Kid's age?" which I thought seemed kind of odd and out of place. Also, he says it after the screen goes black and before the loading screen, adding a lot of emphasize to it. It would explain how The Narrator seems to know every detail about The Kid's adventure and it's not really a stretch to say they resemble each other.