In the Lotus Sutra chapter "Immeasurable Life Span of the Thus Come One", Buddha states -
“You must listen carefully and hear of the thus come one’s secret and his transcendental powers. In all the worlds the heavenly and human beings and asuras all believe that the present Shakyamuni Buddha, after leaving the palace of the Shakyas, seated himself in the place of enlightenment not far from the city of Gaya and there attained supreme perfect enlightenment. But good men, it has been immeasurable, boundless hundreds, thousands, ten thousands, millions of nayutas of kalpas since I in fact attained buddhahood."
Further he states -
At that time the Buddha said to the multitude of great bodhisattvas: “Good men, now I will state this to you clearly. Suppose all these worlds, whether they received a particle of dust or not, are once more reduced to dust. Let one particle represent one kalpa. The time that has passed since I attained buddhahood surpasses this by a hundred, a thousand, ten thousand, a million nayuta asamkhya kalpas.
“Ever since then I have been constantly in this saha world, preaching the Law, teaching, and converting. And elsewhere I have led and benefited living beings in hundreds, thousands, ten thousands, millions of nayutas and asamkhyas of lands."
In other words, Shakyamuni Buddha states he had been enlightened since the remote past, unlike what people believed that he attained Buddhahood for the first time under the Bodhi tree. Since he attained Buddhahood, he had been preaching the Law to countless beings. That should be documentary proof enough that nirvana does not stop rebirth - even the Buddha is born time and again in order to preach the Great Law.