I do not think it is at all true that pre-urban societies aren't capable of complex ontology; someone who feels this way generally has not talked to an actual real live animist about faith matters. I was chatting with one of my students just yesterday about the sweat lodge ceremony as practiced in his home region (the Pine Ridge Reservation), and the symbolism involved in the setting and actions; I would not describe it as any more or less complex than any Christian or Buddhist liturgy, say, that I am familiar with. And as this symbolism was inherent in the way the area was set up, archaeology can confirm that this is not just Settler "contamination".
Lets take a wider and older example: Shamanism, ie Eliade's "archaic techniques of ecstasy". This phenomenon is similar enough around the world that most believe it to have had a single region of origin; it's not just the ecstatic travel itself, but many characteristics connected to it, both practical and mythological/cosmological. When did these ideas spread, and from where? The where is usually assumed to be ancient Siberia. These ideas are already widespread well before the Axial Age, and indeed are old enough that the paucity of the archaeological record around older materials becomes a problem in trying to answer that question. But spread they did, and among peoples that had few of the markers of "complexity" that Europeans look for, not that in fact the forager life is actually all that simple.
At this point we're parsing definitions: what constitutes 'complex'.
If we're contrasting the thought of North American Natives circa 5000 BC with certain Christian sects circa 400 AD there is no comparison. But 'complexity' isn't so much what I was trying to highlight as much as that the degree of specialization is tightly tied to how much of it the society it lives in can support. And so a wealthier society is more likely to host specialized systems of thought. Consider the legal system of Mesopotamia, or the thought of Greek philosophers, the numerous religious sects in Rome.
Further, these societies act as a culture where these philosophies can grow and spread. So it's likely that many of the systems of thought throughout history that still exist today originated in major global centres (China, Rome, India).
I would consult Tainter.
Tainter, Joseph A. (2003), The Collapse of Complex Societies, New York & Cambridge, UK: Cambridge University Press, ISBN 0-521-38673-X
IIRC, he includes Mayan and Chacoan cultures in his examples. Complex civilizations presumably built upon the same sacred traditions as other native Americans.
I think, more closely to the question in the OP: what provoked the axial age. It was that there were societies above a critical mass of population and resources with the ability to propagate their systems of thought.