Cradle of Western civilization IS Greece. Period. Luckily for all of us, Athenians miraculously won at Marathon, that was the end of spreading of Eastern idea of how the world should look like, with millions of slaves working together for the glory of Empire. To simplify, in Western world individual is the basic cell of society, and individual matters, in eastern world, individual is nothing, only small and insignificant part of something bigger, such as family, company he is working for, party or state. The way we look at life and the world around us is 100% born in those small towns in Greece, and was transferred to us through Roman Empire, then Byzantium Empire &Medieval Greek State, and only state in contemporary sense in Europe for hundreds of years) which preserved the culture and knowledge when Roman Empire was destroyed, and in the end, when Germanic and Celtic tribes finally moved from dark ages and entered new period, through Renaissance. So not only that basis of today's western culture and ideas was only born in Greece, it was Greeks that preserved it through Middle Ages until the rest of the Europe was ready to take it.
The first urban centers arose in Mesopotamia, long before anywhere else in the world, followed by the Levant and Anatolia. Eridu, in modern day Iraq, is arguably the oldest city in the world and existed in the 6th millennium BC. Animals and cereals were first domesticated in the Near East, thousands of years before agriculture spread to Europe. Irrigation first appeared in the Fertile Crescent. This rise of urban culture was only possible through structured and complex governments.
We should praise Ancient Greece for its huge contributions to philosophy, but the Greek concept of political freedom can hardly be called the foundation of civilization. Moreover, similar concepts of individual freedom arose in India around the same time, such as in the religion of Jainism. The skeptical Indian school of philosophy called Cārvāka appeared in the 6th century BC (before the rise of Greek Classical culture) and rejected such ideas as the afterlife, reincarnation, religious rites, fate, heaven and hell, and supernatural causes in order to explain natural phenomena: something that sounds surprisingly modern, even today.
Yes, Ancient Greece did produce a highly impressive culture that significantly influenced later 'Western' thought, but a bit of nuance wouldn't be out of place.
*EDIT*
On the point of Marathon: the despotic nature of the Persian Empire has often been exaggerated in Greek accounts (it makes sense to paint a grim picture of one's archenemy after all). The Persian Empire was in fact marked by relative tolerance, as Cyrus the Great realized that repression would cause his huge multicultural empire to quickly fall apart. Who liberated the Jews from Babylonian captivity? Indeed, Cyrus the Great.
