I can name one such civilization : the Olmecs, they were the first known Mesoamerican civilization and they influenced the later civilizations in many ways.
First, Olmec Art is still visible in the art of Mayas and Aztecs: they influenced their art. For example, the Olmecs used Jade, just like the later civilisations.
then, Epi-Olmec script bears some resemblance to the Maya script, so Mayas likely adopted and developed the Olmec script.