A Christian claimed that the Prophet (S.A.W.) received his first revelation while he was sleeping, is this true? And if not, how do we Shias address this claim and provide evidence that this isn’t the case.

We have strong evidence in Islamic traditions on how and when the Prophet received revelation. A person from another faith cannot tell us from their own sources. There is no Muslim scholar in history who has claimed the Prophet received revelation whilst asleep. All the biographies of the Prophet by Muslims established that he got it when he was in Cave of Harra fully awake