As for when he will arrive, there has been no formal announcement concerning his release date. Typically, the gap between new characters being added to the game lasts approximately two weeks. Black Adam would have fallen into that same schedule if not for the delay.
However, we can reasonably assume that Black Adam will arrive some time before Nov. 15 when Season 1 is scheduled to end.
MultiVersus is available on PlayStation, Xbox, and PC platforms.
Source: https://www.distractify.com/p/when-is-black-adam-coming-to-multiversus