Kaido, his promise with Big Mom, King, Queen, his crew all relates back to one place: Punk Hazard.
I personally really like the Punk Hazard arc, I think Vergo was a cool enemy and Law’s reintroduction was amazing. However, Punk Hazard as a place deserves some credit for birthing the Yonko Saga in many ways.
I believe Punk Hazard is where Kaido formed his crew. Kaido has stated he’s been captured a few times, and sometimes prisoners aren’t sent to Impel Down, back before the incident four years ago they were sent to Punk Hazard for testing.
Kaido was sent here in hopes of replicating his power, his almighty mythical devil fruit. Sent here and guarded with Impel down jailers, including King (remember King’s outfit).
So with Kaido here, Vegapunk tested him and experimented on him with his team, including Queen.
This lead to the creation of Vegapunk’s first artificial devil fruit (Momonosuke’s dragon fruit).
Over time he became the leader of these prisoners and the experiments. As we just found out they originally experimented to create beings the might of Oars, who we now know are the Numbers.
I believe that they used the term Oni to describe this project (Demon Ogre) and used the skull of an ancient Giant as their symbol (the warning sign).
Eventually, Kaido decided it was time to escape. However, even with an uprising, and the two turncoats of King and Queen, they couldn’t escape the island. Here’s where the favor comes in. The only person Kaido would know with a crew capable of springing him from his imprisonment is Big Mom and her kids. They probably weren’t “Emperors” at the time, but they were still notable pirates and they escaped Punk Hazard, however, seeing the experiment leads to Big Mom’s and Caesar’s deal down the road.
Now homeless, the new Beasts Pirates need a place to call home. Enter Wano where they find a small island with the skull of an ancient giant. They settle here and name it after themselves, the land of ogres, Onigashima.
*Theory by GreenLanturn73