Climate change is presently believed to be a major catalyst to the development of civilization in Egypt and Mesopotamia. It also thought to have led to the collapse of the Indus River Valley civilization. But it is not thought to have played major roles in the other developments of civilization.
Are you sure about that? From what I have read, climate has a pretty big influence on society, and therefore changes in climate would play major roles everywhere.
In the anthropological context, "civilization" is usually meant to refer to the most complex form of societal organization. Civilizations don't start appearing until about 6000-7000 years ago. By contrast, the Younger Dryas (a sudden climatic shift in the Northern hemisphere that reverted temperatures back to the last glacial maximum) occurred about 12000 years ago. The Laurentide ice sheet probably completely collapsed by about 11000 years ago.
With these definitions, you can see that the distance from the end of the last ice age (collapse of the Laurentide ice sheet) or the end of the last big climate change (Younger Dryas) to the beginning of civilization (~Uruk period in Mesopotamia) is around the same magnitude as the distance from the beginning of civilization to the present day. That's not exactly "soon."
Metallurgy and chariots arrived in China from the west; Mesopotamia, Indus and Egypt were in very close contact. So much so, that the cultural artifacts of the epochs preceding the first dynasties are near identical (including building plans!) : https://raw.githubusercontent.com/wiki/pannous/hieros/susa-e...
Longer quote from The Agricola translated:
> These plunderers of the world [the Romans], after exhausting the land by their devastations, are rifling the ocean: stimulated by avarice, if their enemy be rich; by ambition, if poor; unsatiated by the East and by the West: the only people who behold wealth and indigence with equal avidity. To ravage, to slaughter, to usurp under false titles, they call empire; and where they make a desert, they call it peace.
The bronze age started slightly later--just saying in case that was the next question.