If you use a 6 quart Instant Pot, select the Saute setting. Heat the oil in the pot, add the rice, and cook, occasionally stirring until browned, about 2-3 minutes. Be careful not to burn it.
Add chopped onion and garlic and continue cooking until onion is translucent, for about 2 minutes.
Add the chopped tomato and cook for another 3 minutes.
Stir in carrots, celery, potatoes, and tomato sauce. Press the Cancel button.
Add chicken, water, and salt.
Make sure the Instant Pot is never more than ⅔ full. Lock the lid and close the pressure release valve. Pressure cook on High pressure, setting the timer for 15 minutes. (timer will begin counting once the pressure inside the pot is reached, which might take about 10-15 minutes).
When done, press Cancel and use the quick release method to release the pressure: Turn the valve to allow the steam to escape/pressure to release. When the pressure is fully released, the float valve will drop, and the lid will unlock to open. For safety reasons, the pressure cooker will not open until the pressure is released and the float valve has dropped.
Add chopped cilantro to the soup and check again for salt.
Ladle soup into bowls, including a piece of chicken for each serving, and serve with lime wedges and warm corn tortillas.
Optional: Add slices of avocado to your soup and sliced radishes.