Move the oven rack to the middle position and preheat the oven to 350°F (175°C); spray a 9×13×3-inch pan with nonstick spray.
Heat olive oil in a skillet over medium-high heat until shimmering.
Add chopped onion and sauté for 5–6 minutes until translucent and lightly browned on the edges.
Add minced garlic and cook for about 1 minute until fragrant.
Transfer the onion mixture to a large mixing bowl.
Add shredded chicken, both cream soups, green chile sauce, cumin, salt, and pepper; stir until fully combined.
Lay 4 corn tortillas across the bottom of the prepared baking dish.
Spread 1/3 of the chicken mixture over the tortillas.
Add 1 cup of shredded Mexican cheese over the chicken layer.
Sprinkle 1/3 of the chopped tomatoes and sliced green onions on top.
Repeat the layering of tortillas, chicken mixture, cheese, tomatoes, and green onions two more times.
On the final layer, omit the cheese and top only with tomatoes and green onions.
Mix the remaining 1 cup of cheese with chopped oregano and set aside.
Cover the casserole with foil and bake for 30 minutes.
Remove the foil, top with the reserved cheese mixture, and bake uncovered for 15 minutes.
Let the enchiladas rest for 10 minutes before serving.
Serve with optional toppings such as tomatoes, green onions, oregano, shredded lettuce, or sour cream.