Well, there are almost 4,000 years of difference between the Sumerians and the Aztecs, but the latter certainly had access to historical documents and fossils, though at the time they had little in the way of archeological studies.

In the case of the Aztecs (Mexica) in fact most of the direct history (not archeological) of mesoamerica comes from Nahuatl sources like Tzozozmoc and Chimalpain, we knew they had several libraries and centers of study (the mexica were one of the few civilizations of the time to have a public education system), the largest of which was in Texcoco (sadly burned down by Cortez), not much in the way of archeology, but they did saved reverence for ruins and ancient (to them) structures, like in the case of Teotihuacan.

As for fossils, they did had them, for example, the femur of a Mastodon was given as a gift to Cortez by the Tlaxcaltecans, but like the Europeans of the time they often attributed them to the remains of giants from the mythical past.