If humans evolved from Mesoamerica, animal domestication would have been dramatically slower. The chart on page 160 shows that the "major five" domesticated animals lived in the Eurasian region. Along side that, humans would have to travel for an even greater period of time to reach the Fertile Crescent.
Beginning from Africa, humans had the great advantage of having many plants and animals nearby. The Fertile Crescent was rich with plants that hunters and gatherers were able to harvest. Eurasia also had many animals that were rich in protein. Had humans evolved from Mesoamerica, the end result would not be the same. Thousands of years would pass by with no sign of settling. Humans would only be able to hunt and gather because of the lack of big game. Animal domestication also has a huge impact of the ability to farm. Not only were the animals found in Eurasia (such as sheep, goats, cows, etc) a great source of food and milk, but they were also a great source of fertilizer. This fertilizer was a valuable source to have when early humans were beginning to farm. The fertilizer made farming easier. Not only did the humans themselves unknowingly begin to domesticate plants, but they were also finding useful tools to grow them faster. However, the lack of these animals in Mesoamerica would mean that humans would spend more time searching for food rather than developing into a greater society. A steady source of food is key to creating a civilization. Along with meat, milk and fertilizer, the Eurasian animals also provide wool and leather. While migrating to a colder climate, these things would have been incredibly useful. Imagine beginning from Mesoamerica and migrating towards Alaska. Warmer clothing would be essential to surviving. Without warm clothing and a steady food supply, humans would undoubtedly die. Although water buffalo were available, I doubt it would be enough to support a large group of people migrating such a long distance. Plants in the Americas also took longer to grow compared to wheat and barely found in the Fertile Crescent. If humans couldn't supply the needed amount of food for themselves, they would certainly not be able to sustain livestock. Humans would not be able to domesticate animals if they had no means of feeding them. The Fertile Crescent provided more than enough grain to sustain humans and their livestock. Since humans originated from African, we were able to take advantage of the animals available to us in order to adapt to the conditions around us. Overall, it would have taken humans much longer to cover all of the world due to the lack of resources. The longer humans remain hunters and gatherers, the longer it would take for functioning societies (as we know them now) to form.