The Aztecs believed that our world was created 5 times, and 4 times destroyed before; these are the so-called "Five Suns". I know that the present epoch by the Aztec calendar, i.e. the "Fifth Sun", began on 3113 BCE. What are the dates of the previous 4 "Suns"?
The 3113 BCE date comes from the Classic Maya calendar. According to the ancient Maya, the current baktun, or creation period, started on August 11, 3113 BC, written in the Maya calendar system as 0.0.0.0.0 4 Ajaw 8 Kumku. The date and its significance are explained in the inscriptions of Palenque, Mexico, and Quirigua, Guatemala. It looks like someone is borrowing from the Maya to date the start of the Aztec First Sun. In fact, the Aztecs did not date the start of the First Sun in any form that modern scholars can recognize.
Each of the preceding Suns lasted 2028 years, at least according to the French wikipedia (which has some more details):
"The total number of years for the first four suns is the same: (2028 years), but the distribution is different: (676-676-364-312) for the Historia de los Mexicanos and (676-364-312- 676) for the Leyenda de los soles. It is each time multiples of 52, that is to say the number of years corresponding to an Aztec 'century'."
This is an interesting question. I'm not sure there's an actual start date for the 5th sun according to any scholar, but that is a task I'd like to investigate further. However, I'm not quite sure there will be one. Take for example Greeks and Romans. While there's a myth that relates their cosmogony, there's no date that accounts for it. Rather, the time is actually accounted starting on the foundation of their cities. Take Rome for example. Aztecs did the same. I guess it's like trying to determine the date of the creation according to the judeo-christian bible, which by the way Isaac Newton tried in his time.