What kind of factors did create the intellectual explosion that did produce the precursors of modern science, philosophy, poetry, literature and architecture in Greece of Antiquity? It was a sudden and unexpected outburst of creative energy. Nothing like it had ever before been witnessed in human history.
The answer can be for a big part lie in the nature of religion that the Greek did adopt. This religion allowed all new kind of intellectual curiosity. This freedom of thinking made it possible to present all kinds of new ideas. Overall the Greek religion did extremely rarely interfere with the intellectual life in Greece of classical times before the advent of Macedonians and Romans.

Of course, the swift economical development in Greece was a major force that made possible the creation of a free class of intellectuals. The general open atmosphere of a trading empire did also favor intellectual development. However, this idea of religion as a decisive factor does become much clearer with a direct comparison with a society of similar age and very near geographical location. It was a place where religion was a clear hinder for mental development and did erect direct limits for intellectual curiosity.
A sad state of affairs does come visible when one does compare the achievements of early followers of Judaism and Christianity with the achievements of the even more ancient Greeks. Those Semitic nomads who did give us one of most important 'Holy Books' did, in fact, accomplish next to nothing in fields of culture, science, philosophy or political ideas compared to the Greeks of the same time.

These semi-nomadic tribes did not, in fact, create no memorable works in fields of arts, science, poetry, visual arts, music or technology. On the other hand, the base for our current science, philosophy, arts and technology was created in the Greece of Antiquity.
It is impossible to see the inhabitants of ancient Judea that they would have left any real visible marks in the development of the western civilization other than the Old Testament and a large stack of various religious texts. The science, philosophy and arts that were in created in Greece can fill entire libraries. On the other hand, the whole intellectual heritage of the Jewish semi-nomadic Semitic tribes can be crammed into one book. This book has in reality extremely little to give for people who live in a totally different and in every aspect more developed world.

 The Temple of Hephaestus in Athens is the best-preserved of all ancient Greek temples. - Wikipedia

A very basic clue for this dilemma can be found in the different concepts views on Gods and religion that the Ancient Jews and Greek did have. The gods of Greece were more of a theatrical assembly. They did not show a direct interest in the matters of any living individuals.
The Jewish people did believe that their angry and vengeful personal god did observe them closely every single moment of their life. They did even believe that this deity could monitor everything they were doing or even thinking. This situation gave the people of Greece at that time a totally different chance to think freely. At the same time, the Jews just had a book that already had all the answers they needed. There just was no need to discover or even look for any new explanations.

The Greeks of Antiquity created a tremendous amount of culture, science, architecture, poetry, plays and philosophy, but all that Judea could produce was Judaism from which did eventually also Christianity rise. A very basic reason for this glaring disparity between these two civilizations was the completely misplaced belief that was held by early Jews and Christians that all the central truths that humans do need had been already found and discovered. They were to be found in a single one old book, to which Christians did later add a major new part that did support their newfangled religious ideas.
The quite complete general intellectual impotence of both the Jewish tribes before their final destruction in the first century and of the early Christians outside the realm of creating of religious literature has been hidden from view by much, much later achievements of the followers of these two religions.

These later successes were, in fact, mostly a result of remarkable lessening of the grip that these religions did have on the minds of people. In the Christian world this process of freeing the minds started with Renaissance. It got really going with the Age of Enlightenment. The next new big explosion of new ideas in science, philosophy and arts was experienced after a thousand years of Christian stagnation.
This event was, in fact, quite like in the ancient era of intellectual freedom in the Greece of Antiquity, where religion did not meddle in the intellectual development.

(This piece was completely refurbished on 10th of January, 2013)