Kaido has been in Wano for two decades. The only thing that was left to take over eight years ago were outlying places like Ringo he didn't even care to conquer himself as he sent weaklings to do so that would be repelled by a fox alone. Nothing stopped him from having some happy time with a woman eight years ago and engendering a son who'd live in Onigashima.
Also, Big Mom raised and established as a pirate as she constantly gave birth and got pregnant over and over, and she was the one pregnant while Kaido only needed to spread his seed. Even if Kaido was taking over Wano and expanding his empire eight years ago, there's no excuse for him to not get a girl pregnant considering Linlin's feat.