In Chapter 1013, Kaido defeats Luffy for the 2nd time and as he’s falling off Onigashima, Kaido says “Looks like you couldn’t be Joy Boy either.”
This implies to me that Kaido thought someone else was Joy Boy before, but that hope was dismissed. I also believe Kaido thought that Joy Boy was himself.
In Chapter 1035, when Kaido saves King (who is very handsome), he tells King that ONLY HE (Kaido) can change the world. I don’t think that was overconfidence. Kaido really seemed to think he was Joy Boy or that he could be Joy Boy.
But some event after that proved to him that he wasn’t Joy Boy.
I think ever since Kaido knew that he couldn’t be Joy Boy, he began to search for someone who can actually be Joy Boy.
In Chapter 972, Oden tells Wano that 20 years later Joy Boy would come to Wano, but Kaido didn’t react to that at all. Almost like he already knew this.
I believe Kaido is in Wano to see who Joy Boy actually is. To see what Joy boy has that he doesn’t. To see why this person can be Joy Boy, but he couldn’t. So he invaded the one place he knew Joy Boy would definitely come. Wano.
In the Marineford Arc, we know that Kaido was on his way to Marineford with King to fight Whitebeard. But what if it wasn’t to fight Whitebeard? What if it was to save Ace?