Originally, Shazam! - Fury of the Gods was supposed to shoot at the same time as Black Adam, but we have no idea whether that will still be the case. Even if cameras do still roll simultaneously, there's nothing to say any sort of crossover will be filmed, but the prospect certainly excites star Zachary Levi.
Shazam! featured quite a few references to Black Adam, but when Levi was asked on Dan Fogler's 4D Xperience whether there are plans for his DC Comics character to square off with Dwayne "The Rock" Johnson's Black Adam, he responded with a laugh: "That's well above my pay grade. I have no idea."
"The Rock is his own planet. He kind of does whatever [he wants], The Rock does what The Rock wanna do. So we'll see how that all plays out. But per the comic books, Black Adam and Captain Marvel - my true namesake - they're yin and yang to one another. They are identical."
Levi would later admit that the similarities between Shazam and Black Adam led to him believing Warner Bros. would find an actor closer in appearance to Johnson. Now, though, he's just excited about some sort of crossover. "Black Adam is from the Captain Marvel/Shazam part of the DC universe, so I hope [they meet]. I think that would be awesome to be able to go and do that."
"[Johnson] [is] doing his deal, the Black Adam stand-alone, and we're gonna do our sequel [Shazam! Fury of the Gods], and we'll see what goes from there," Levi concluded.
A meeting between these two is inevitable, but it seems like the plan is not to rush anything and have Shazam and Black Adam cross paths only when it feels like a true event for fans.