They watched the sun. They knew about solstices (high point, low point of sun in sky). They tracked how many days between the solstices. They were interested in this because it correlated with growing seasons.
None of this happened overnight. There is always a large amount of trial and error involved in the development of ancient calendars. The idea of a leap year was a ‘fix’ to a calendar that wasn’t quite right. It seems like it happened instantly but if you look back, the trial-and-error time was often quite lengthy.
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