Where people living in Mexico at the time America was discovered?

When America (specifically, the Caribbean islands) was discovered by Christopher Columbus in 1492, Mexico didn't exist as a political or geographical entity in the way we understand it today. The Americas were inhabited by various indigenous peoples and civilizations, but the region presently referred to as "Mexico" was home to a number of Mesoamerican cultures and civilizations, including the Maya, Aztecs, Zapotecs, Mixtecs, and others.

At the time of Columbus's arrival in the Americas, the dominant civilization in the area of present-day Mexico was the Aztec Empire, also known as the Mexica civilization. Their capital city was Tenochtitlan, located on the site of modern-day Mexico City. The Aztec Empire had an advanced civilization with significant developments in art, architecture, agriculture, urban planning, and religious beliefs.

It's important to note that the term "America" was only applied later to refer to the continents as a whole, and its usage did not exist during the time of Columbus's voyage.