How did Olmec civilization differ from Maya civilization? The Olmecs were the first culture to live in Mesoamerica. The Mayas came later and adopted some of the Olmecs' early practices. The Mayas were the first culture to live in Mesoamerica. The Olmecs came later and rejected most of the Mayas' early practices. The Olmec civilization declined after a prolonged drought, while the Maya civilization continued to flourish into the 1500s. The Maya civilization declined after a prolonged drought, while the Olmec civilization declined after years of warfare.