Africa is were we say everything started out. But what changes would have happened if instead of Africa it all started in Mesoamerica? How different would things be? I've thought about this for a while after having read the question. And I have come to the conclusion that not much would have changed.
The only thing different would have been the animals. There are different types of animals in Africa and Eurasia than there are in the Americas. But still I don't believe that could have made a difference because Diamond says that animals evolved alongside humans and so whatever animals were there were the ones that would have evolved with the human.
Eurasia would have still been dominating because they still would have had the animals like horses and cows and others that would have really impacted their community. The Americas wouldn't know much about civilizations while the Eurasians would have.
It stared in Africa and it still didn't become the dominating county so why would things if it all stared in the Americas. The fertile crescent would have still been on the other side of the world so it still would have been hard for them to produce crops even if they did have the animals to do so.