In Deuteronomy(4:32-34), two points are made in reassuring Israel that God has not abandoned them. The reader is tasked with searching from one end of the heavens to the other to see if a God ever spoke to a nation of people who lived as the revelation at Sinai claims, or if a God ever deigned to take one nation from another as He did in the Exodus narrative.
This Quora answer mentions a developing theory that supports the occurrence of an exodus-like event within Egyptian history. This question will not deal with the uniqueness of this event.
Rabbi Kelemen discusses the uniqueness of the revelation at Sinai. One of the points he asserts is that which is asserted in the Torah above; that there is no instance of a revelation of God to a nation that the nation survives. Kelemen claims to have examined all other known religions and found none that have made the same claims, though he says that a sect of Hare Krishna believes in such a revelation, but all of the witnesses to the revelation died shortly afterward, which make the claim fall short of the Sinai Claim.
This answer to a related question on Skeptics Stack Exchange provides some examples of Native American traditions that seem to make the same claim as the Sinai Claim.
The Aztec Huitzilopochtli Myth and revelation of Huitzilopochtli tells that the Aztecs, who settled in Lake Texcoco, believed themselves to be descended from tribes of immortal people from Aztlan until they had to leave as instructed by their god Huitzilopochtli who took the form of a white eagle. (It is flawed because it is unclear if a God or a bird came to the people, or if the revelation was only with the priests.)
The Fifth Creation of the World by Marumda and the Pomo tribes tells that the god, Marumda, created the world five times (the first four destroyed due to sin), and that the Pomo People, a group of tribes in California that exists today, were created the fifth time. All of the Pomo villages were planted by Marumda and he revealed himself to their ancestors, sometimes accompanied with miracles, and taught them how to survive and behave and taught them dances that are still performed today. (It is not completely clear, however, how massive the initial size of the population that Marumda created and was revealed to was, and it's not clear if Marumda spoke to the entire nation at once.)
Revelation of Gitche Manitou at Pipestone, Minnesota tells that the Sioux Indians had a divine revelation of their god and creator Gitche Manitou at the Pipestone National Monument to all the Native American tribes. He breathed into a peace pipe he formed and made a large smoke signal that beckoned all the tribes to gather. They had spite between them, but Gitche Manitou chided them to do away with their weapons, behave properly, and make peace. After this, before all the nations, Gitche Manitou ascended to heaven amidst the smoke. (The source in the answer is a poem based upon legends, however, so it is more difficult to ascertain for certain that the Sioux people actually believe this as history.)
The Lakota legend of White Buffalo Calf Woman tells that the Lakota People witnessed their god Wakan Tanka (same as Gitchie Manitou) reveal itself to all seven tribes of the Lakota as White Buffalo Calf Woman. Two hunters went to look for food. They saw a beautiful woman floating towards them. One of the hunters desired the woman and was turned into a pile of bones amidst a cloud. The other hunter became afraid and prepared to shoot the woman, but she couldn't be harmed. She informed the hunter to return and have the Lakota prepare for her arrival. When she arrived, she taught the Lakota how to behave and perform all the sacred rituals and gave them a sacred living pipe that is still guarded to this day. As she left, the people saw her turn into a black buffalo, then brown, then red, and then white, which is sacred. As she disappeared, large herds of buffalo appeared where she was and allowed themselves to be killed for the Lakota to live. (The size of the Lakota nation at the time of the revelation and miracle is not so clear.)
(The answer provides two other instances that do not come close to the criterea in Deuteronomy of a God speaking to an entire nation who survived the event, so I did not address them.)
Does Rabbi Kelemen (or anybody else) address these directly? The seem to have some flaws, but I was wondering if anyone really researched these claims and came up with real conclusions.
How are these similar claims addressed per The Torah's claim to the uniqueness of the Sinai Revelation?