I will try to explain Kaido’s character and what led him to where he is today.
Starting from the beginning, we can see Kaido as 10 years old. A boy who seems to have been born on the battlefield and the only thing he knows is to fight and is hungry for more.
At age 13, he is sold by his own country to the Government to become a Marine (the same was going to happen to Big Mom). He says he’s no bargaining chip and doesn’t want to become a Government dog. His country did this in order to continue participating in Reverie.
Kaido escapes from the navy ship and is said to let himself be caught in order to eat. Maybe that’s where the part of Kaido being captured 18 times came from.
When Kaido is 15 years old and at Rocks’ request, Whitebeard asks if he wants to become a pirate and join the crew. Kaido accepts.
At age 21, the God Valley incident occurs. From the dialogue, it seems that some opportunity has arisen for the Rocks to achieve something. Garp is said to have defeated the Rocks (Roger’s name is not spoken by the pirates present at the Rocks base). After this moment, we only see Big Mom worried looking for Kaido. Perhaps Big Mom gave the fruit to Kaido to the point where he joined her crew (Oni race) and he fled without a trace (hence the conflict between the two).
This information was only taken from Chapter 1049… but there is something it doesn’t show which is the 10 years that have passed since the God Valley incident until the time when the old witch goes to speak with Kaido. However, there is a small flashback in Chapter 1035. In this chapter, Kaido tells King that he is the only one who can change the world. It seems that they had already spoken before this moment. Upon leaving it looks like they are in a Punk Hazard lab and Kaido names him King.
After that comes another flashback in Chapter 1036 where Kaido asks King if he thinks he is Joy Boy. And here’s the twist, Kaido isn’t the one looking for Joy Boy, but King. King in Chapter 1035 asked if Kaido could change the world, because he is the one waiting for Joy Boy (the one who will change the world). In Chapter 1036, King says that legends are legends, which means he no longer cares about Joy Boy, as how Kaido saved his life (changed his world?) Joy Boy no longer matters to him. Kaido never wanted to be Joy Boy either, he just asked King if he would be the figure he (Lunarians) has been waiting for.
We now return again to Chapter 1049, where the old witch proposes something to Kaido (going to Wano). It is also in this part that we observe Kaido’s true desire. He wants a big war (as he said in his first appearance) that involves the whole world. He adds that it is only in war that the value of each person is seen. Kaido is a character who believes in the law of the strongest, in the idea of a king of the jungle, king of beasts as his name says. After observing the rot of nobles when he was little (selling to even worse garbage) and perhaps having observed something in God Valley (protection from Celestial Dragons, weak and rotten beings that are literally the opposite of Kaido’s mindset), he came up with this idea of a world where only the strong stand over the weak. It’s a nice parallel to what Law says to Tashigi in Punk Hazard.