Place the chicken thighs, bell pepper, tomato, and green chiles in an Instant Pot cooking container. Pour the chicken broth and tomato sauce on top and sprinkle with the chili powder, ground cumin, chipotle powder, smoked paprika, and garlic powder. Season with salt and black pepper, to taste, and stir to combine.
Add the lid and lock into place. Flip the pressure valve to “Sealing” and select the “Manual” setting on high. Adjust the cook time to 10 minutes.
When cook time is complete, allow the pressure to release naturally for 10 minutes before doing a quick release of any remaining steam.
Remove the lid and carefully transfer the chicken thighs from the Instant Pot to a plate. Shred the chicken with two forks and return to the pot. Add the Mexican cheese a little at a time to avoid clumping and then the cilantro. Stir until the cheese is completely melted.
To serve, ladle the soup into individual serving bowls and garnish with some fresh cilantro, Mexican cheese, and chopped avocado. Serve immediately with lime wedges for squeezing, if desired. Enjoy!