Man of Spoilers

By the end of, "Man of Steel," it's revealed that Superman's biological father, Jor-El, embedded the Kryptonian Codex in his son's cells. That means he's the living library of their entire genetic heritage. It's also revealed that the Codex could still be deciphered if Superman were deceased. At the beginning of the movie, Jor-El steals the Codex, which is in the form of a skull fragment with writing on it.
That means that potentially, at some point, Superman could have traveled into the past and died, leaving behind a piece of his skull, which is then used to populate Krypton and birth his own descendants, including himself in a circular pattern.
Also, this is Cyborg Superman:

Notice how he's missing a part of his skull.
While the movie illustrates how Superman gained control of his powers, at no point does it reveal how he knows to fight. In fact, the movie goes to great lengths to teach us how Superman never stood up for himself until the moment he has to fight the Kryptonian soldiers, who have the same powers he does, but with decades of combat experience. How does he manage to hold his own against them if he's never thrown a punch?

In the comic books and cartoons, an adolescent Superman goes into the future to help the Legion of Superheroes and train. Upon returning home to Kansas, he has his memories wiped clean. Meaning he's already traveled through time and will do so again in the future.