Everybody is calling out that it's Oden, but I think some of you are overlooking that it could also, and I'm not kidding here, be Momonosuke. We can't overlook the fact that this arc introduced TIME TRAVEL, even if it's only in a very limited form. As Oden's son, Momonosuke would obviously end up a lot like him in twenty years, would he not? Likewise, Oden wouldn't know anything about Luffy, but if at some point in the future Momonosuke goes back in time to where he actually belongs, and then all of this happens to him, then obviously he would "be waiting" for Luffy. We have questions about the circumstances surrounding all of this that have NOT been answered, and Momonosuke is involved in them: why does he have an animal form identical to Kaido's? Why is it that when Kaido seems to transform, Momonosuke also does, and when he turns back, that's when Momonosuke also turns back? We know Vegapunk is heavily involved with Kaido, and it is Vega's experiments that pushed the boundaries of what is and is not possible with Devil Fruit powers. Someone like that would naturally be very interested in any fruit with the power to send people through time, even if it was only in a very limited way. And we already got a confirmation before this arc even started that some form of time travel will almost certainly take place in the future as well, because the True King of the World has an old and crumbling version of Shank's hat.
Don't forget, every time Kaido has seen Momonosuke, he gets a closed look on his face and doesn't talk. It happened in this very chapter, even. Kaido knows something that Orochi and everyone else do not. I don't think Momonosuke is secretly is son, because if that were true then Kaido wouldn't let them treat Momonosuke so badly, but there's a lot about this we still don't know, and Momonosuke is right in the middle of it. We still have no explanation for how he has Kaido's fruit power, or why the two of them seem to be connected.
Maybe I'm overthinking it, but given everything that's happened so far in this arc, I find it more plausible to believe that Yamato is an adult Momonosuke than him being Oden.