Well, yes we are dead in sin in ourselves.
But where do you get your idea that Calvin said belief comes after being born again?
I don't know any Calvinist who believes this and I don't know where you got the idea.
Book three of Calvin's Christian Institutes for starters. Calvin repeatedly emphasizes that regeneration precedes and enables faith. Otherwise faith is just another work. Also, those sections of Book two regarding justification and free will. Luther made the exact same points in his "Bondage of the Will"