Heat the oil in a medium skillet over medium-high heat. Add the turkey and season with 1/2 teaspoon salt and 1 1/2 teaspoon pepper. Cook, breaking up with a spoon, until no longer pink, 5 to 6 minutes. Pour off any excess liquid. Stir in half the salsa and cook until heated through, about 1 minute.
Meanwhile, in a small bowl, combine the remaining salsa and sour cream.
Divide the lettuce, chips, turkey mixture, beans, avocado, Cheddar, and olives (if using) among bowls. Serve with the salsa-and-sour-cream dressing.