Your question assumes something that isn’t true. We do, in fact, have an extant written record of pre-Columbian history in Mesoamerica. There are hundreds of existing Nahuatl codices describing the history and culture of the Aztecs, though most if not all postdate the conquest. This is largely due to the fact that the Spanish, during their takeover of the Aztec Empire, destroyed libraries of Aztec codices and other writings to the point that almost none survived. And even prior to that, the Aztecs had numerous written works burned upon taking power. But post-conquest writers were still familiar with the histories of the empire, and from their writings we can piece together a coherent narrative of its history. (I highly recommend Camilla Townsend’s Fifth Sun for this - it’s an account of Aztec history based entirely on Nahuatl sources).

For the Maya, it’s somewhat different, but we do have four surviving pre-conquest Maya codices. It should be noted that these are only a fraction of what would have existed. Others have been discovered in archaeological digs but are essentially unreadable; but the majority of Maya codices were victims of the Spanish conquest. In particular, bishop Diego de Landa had a huge number of codices and other Maya writings burned, and over the course of the Spanish conquest the vast majority were lost to history. However, codices are not the only written records we have. Many Maya sites have stelae containing descriptions of important events, such as a list of rulers or of important actions during a ruler’s reign. Through these records we have been able to piece together a fairly solid history of some prominent Maya cities like Tikal.

Mesoamerica is the only region of the Americas with a writing system that resembles that of the Old World, but it was not the only one with a form of recording its history. The peoples of the Andes used the quipu, a knotted string that could be used to record information - including, quite possibly, history. Unfortunately, the ability to read the quipu appears to have been lost not long after the Spanish conquest. North American communities on the Great Plains kept winter counts, which were pictorial calendars recorded mainly on buffalo hides. Each year was represented by a pictograph depicting important events of that year. To the east, along the Great Lakes, the Anishinaabe peoples kept wiigwaasabakoon, birchbark scrolls used to record history. For instance, the Ojibwe recorded their migration west to the Great Lakes on these scrolls. There’s some evidence that similar recording devices may have existed across more of North America, but there’s not strong archaeological evidence (wood does not preserve well, anyway) and in the wake of colonization a lot of communities would have lost not only the ability to interpret such writings but also the writings themselves. (The Ojibwe, however, do still possess some of their birchbark scrolls).