The question of the Mayans and Aztecs is tricky and liable to misplaced enthusiams, and this isn’t perhaps helped by the tricky complexity of the model used to analyze the question. But it is the same ‘stream and sequence’ model discussed here many times.
http://darwiniana.com/?s=stream+sequence: the many links on the stream and sequence model.
The issue arises in any model where a set of discontinuous short transitions is embedded in a continuous stream. This model is very helpful in sorting our world civilization, suggesting the model is onto something,despite crudities.
So the stream of Canannite history shows the embedded ‘transition’ recorded in the Old Testament, being careful to see that most of the history in the Bible is the ‘stream’, while the ‘sequence’ is only the short period 900 to 600. This is artificial but it explains so many things it is uncanny. In ancient Greece we see the same, along with India, and China. Note that in China, far from the mainline the onset of the Shang in the stream then shows the (almost invisible) sequence phase, and, sure enough the core texts of the Chinese tradition, viz. Confucius, source in the bullseye here. This analysis shows two cases: the stream onset by diffusion of a new culture line, e.g. the Mycenaean, (and the Cretan, and umpteen other cases), and the sequence arriving in a fixed time slot: e.g. the sudden take off in Archaic Greece.
All this analysis fits perfectly with the New World case, where the Olmec corresponds to the middle period Mycenaean, Shang, etc…The Persian, Roman/Italic?, Greek, Israelite, Indic and Chinese. The Indic is confused by the Aryan invasion question but is nonetheless clear. The Persian case (we forget that monotheseism is a Persian/Israelite (Egyptian) construct.
So the Olmec is a diffusionist middle period startup and this field spawns the context for the Mayan period, so tantalizingly in parallel timing with the Axial cases.
It is eerie and hard to figure: one should simply see that a model, if it can clarity something, gets advanced a giant step, but the foundation may remain mysterious: the whole issue of synchronous emergence.