It's possible the Mayans referred to previous civilizations as previous humanities. And they might indeed have thought in terms of Humanities as representing a step above Savage and as such Humanities were to be represented by superior symbols.
It would certainly make sense to see the influence of Sea People on the decline of the Bronze Age and the rise of the Iron Age as a movement from one Humanity to another Humanity. Here you'd have to think of a Humanity as a description of how we people arranged ourselves so that together we might be in the world as a Humanity, a collection of people, rather than a civilization.
But no! Civilization is defined this way : a descriptive term for a specific type of large-scale, complex social and economic organization. The specifics are thus : urbanization, food surplus, division of labor, social stratification, record keeping, central government.
The first recorded civilizations begin to appears 4 to 6,000 years ago. They include remains of towns and cities along Mesopotamian rivers, again along the Indus Valley, in South America, can't forget the Ancient Egyptians 5000 years ago, there's the sacred city of Caral on the coast of Peru and the Mayans of Central America who flourished and floundered from 2000 BC into 250 AD
As far as we know Humanities began to appear around 300,000 years ago.