They get this story from recorded traditions which will need an equally recorded tradition/historical account [if there is one!], to refute this. I do not think the following verse will have any effect; who puts the Quran ahead of the infallible historians?!
25:32 Those who are bent on denying the Truth ask, “Why has not the Qur’an been revealed to him all at once?" But that has been so! For, in order to strengthen your heart We have already arranged it in the Right Order. And We have caused you to convey it to people in stages, step by step.
Arranged in the right order, Surah1,2,3 ....114!
The wāḥidatan [all at once] is an accusative feminine indefinite noun which means it is asking why they are asking why it was not revealed all at once. The stages mean they were able to digest what was being revealed before something else came down.