Heat olive oil in a large skillet over medium-high heat. Once hot, add the red onion and cook for 2-3 minutes or until softened. Add the corn, zucchini, cumin, salt, and pepper; mix well and cook until vegetables are just beginning to brown, about 4-5 minutes.
To the skillet, add the chicken and salsa; mix well and heat through, about 3 minutes. Stir in half of the cilantro and remove from heat.
Spread 2 tablespoons of crumbled cojita over each tostada and top with the hot chicken and vegetable mixture. Serve immediately, topped with remaining cilantro.