Klaus survived the apocalypse
In season 3, he realises he had immortality. That doesn't mean he never had it.
So, In Season 1's end of world, Klaus was in the world, Like Five. Except, He must've been surrounded by his dead family. So he must've had the guidance of Allison, Vanya (As he was Vanya at that point.) Luther, Diego and as always, Ben.
So, Did Klaus change his identity, And become a new person in the commission? Or did he live forever.