In the games, specifically Halo 3, Truth hints that humans are the actual Forerunner, Johnson says, "What, can't start your own party," to which Truth basically says: I can't light the rings, because only your race, whose ancestors made the Ark, and therefore are the Forerunners, can. Or at least so far as I can tell from how the dialogue goes.
The 343 stories tell a different tale. Humans are as old as the Forerunners, but were basically wiped out by the actions of the Forerunners as they tried to finish off the Flood. Again, so far as I can tell.