There seems to be no evidence of any cheese being produced that I know of within Mesoamerica, at least. Sophie Coe does not mention any kind of milk product in her book America's First Cuisines (1993) which covers Aztec, Maya, and Inca foods before contact.

Edit: I am curious as to whether some native groups did pick up dairy farming post-contact when they had access to dairy producing animals and what sorts of things they did produce.

In 1521, a man later named Francisco de Chicora was captured by the Spanish in what is now South Carolina. He eventually went to Spain the company of Lucas Vázquez de Ayllón, the leader of a few failed expeditions to colonize the Carolinas early in the 16th Century. While in Spain, Francisco spoke with the historian Peter Martyr and described his homeland. While Ayllón vouched for Francisco's veracity, Martyr (and modern historians) found reasons to question the truth of Francisco's descriptions.

Among his more dubious claims was his description of a territory called Xapida, which the Spanish described as full of deer. Francisco elaborated that many of Xapida's deer had been tamed. The fawns were kept in pens or in people's home. The does were allowed to roam as they pleased, but would return to nurse their fawns and would allow themselves to be milked. From this milk, the people of Xapida would make cheese according to Francisco. He also claimed that the Xapidans kept chickens which are not native to North America, among other birds.

This portion of Francisco's description of the Southeast coast is currently unsupported by archaeology or other historical sources, though in recent years it the "Testimony of Francisco de Chicora" has been a favorite of pseudo-historians attempting to identify an alleged pre-Columbian Irish colony in the region (though they usually ignore Xapida in favor of neighboring and politically dominant Duhare). If you're looking up Native cheeses, the vast majority of sources in support of such ideas will eventually lead you back to Francisco de Chicora's dubious claims.

In case you're curious about why Francisco would spin such tall tales, Ayllón was eager to dispatch another expedition to the region and Francisco was his main marketing tool to drum up support. For his part, Francisco seemed to have supported the idea of a future expedition as a means of returning home. As soon as he lead Ayllón back to South Carolina, he escaped from the Spanish and was never seen again.