How do you think the Olmec was able to influence the Maya civilization, which did not emerge for several centuries after the Olmec had faded?

Even though the time period between the fall of the Olmec civilization and the emergence of the Maya civilization is relatively big, the Mayans were still people that had their civilization based on the Olmec civilization. This was possible because the Olmec were the most advanced of all people in Central America, and their culture, religion, way of life, were adopted by the surrounding civilizations. As the Olmec civilization came to an end, their traits continued to live in the people that adopted them, as well as the people from the Olmec civilization itself, since they did not just disappeared from the face of the Earth, but disintegrated into multiple tribes. The Mayan ancestor were ones of the people that adopted the Olmec ways, so the Mayans just made slight modifications as they were becoming more developed, thus making them a civilization that spread the Olmec ways even more later on in the history, and influence even more people in the region.