Preheat oven to 350 degrees F (175 degrees C). Grease a 7x11-inch baking dish.
Bring a pot of lightly salted water to a boil; stir in squash cubes. Reduce heat to low; simmer squash until slightly softened, about 3 minutes. Drain and set aside.
Mix cream of chicken soup, sour cream, butter, carrots, and onion in a bowl until thoroughly combined; stir in 2 cups of stuffing mix and the squash. Transfer to prepared baking dish. Sprinkle top of casserole with remaining 1/2 cup of stuffing mix.
Bake in the preheated oven until bubbling and squash is tender, about 25 minutes.
