Technically it is possible to give the Americas and Oceania a fighting chance with increased trade between them. If I were to do a very basic timeline, it would go something like this.......................................................................
(1) Americas= They already have the llama,guinea pig and muscovy duck as domesticates, plus at least two viable agricultural crop packages. And there are other domesticable animals, the paca,agouti,chinchilla,mara,hutia,pudu,
chuckwalla and several species of parrots. More tricky but maybe manageable would be domestication of peccaries and rheas. And it's not that far of a stretch for some tribes to domesticate jaguarundis and ocelots as verminators or some other New World small cat. The Andeans had some good boats and likewise the Carib were fairly successful in the Caribbean. And the Arawaks were very resourceful as well. So maybe a crisis of sorts, perhaps a war,populasion explosion or bad politics to necessitate trade, maybe looking for allies against powerful enemies even?
(2) Oceania= Meaning Melanesia,Micronesia,Polynesia and Australia. The Polynesians are among the worlds greatest navigators and the Melanesians and Micronesians aren't too bad themselves. They have chickens,pigs and the poi dog as livestock.
As always, Australia got the short end of the stick in that regard, yet the Aboriginals are very resourceful and inventive. We know that in the southern part of Australia practiced a form of aquaculture, digging weirs and trapping eels, plus used fire-stick farming. So it's not that far off that they can cultivate some wattle trees like the Golden Wattle and/or Black Wattle and some types of yams. In fact Australia has quite a few domesticable plants. And they have some birds that are good for that as well, emus,brush turkeys,bustards and again parrots. As for the northern part, well it's a good thing that the Makassans traded with the Yolngu and maybe earlier contact could've lead to a more maritime culture. Also contact with the Maori would've been mutually beneficial, likewise contact and/or trade with one the New Guinean tribes.
Anyway, for the rest of Oceania, I'd say a population explosion or some bloody conflict that necessitated further exploration and trade.
(3) Contact and trade between Oceania and the Americas. Or rather, greater and more frequent. Definitely plausible given what we know about the Polynesians and to be honest, several Pacific Northwest Tribes are pretty good in their canoes as well. So let's say that the Rapa Nui thrive and colonize other nearby islands. They conduct trade with the Andean people and Mesoamericans and is a way for crops and livestock to be exchanged between North and South America. And as a bonus, Andean crops and livestock reach New Zealand.
(4) Increased contact with Indonesia and Siberia. Reindeer domestication would help in the Arctic at least. Hell, a surviving Vinland is a good thing for both Norse and Native Americans alike.
Anyway, this is a bare-bones idea and even then I doubt that the Americas and Oceania would have the edge over Europe,Asia and Africa because the Old World is older, has tons of history,conflict and spreadable disease between them. But it would be neat if they a fighting chance.
And yes I'd love to see Ice and Mice/Land of Red and Gold scenarios in this situation.