Select the Sauté function on the Instant Pot and add the olive oil.
Add the ground beef to the inner pot and cook until browned, using a wooden spoon to break the meat into small crumbles.
Add the diced onion and bell peppers to the pot; sauté for 4 to 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and cook for 60 seconds until fragrant.
Pour in 1/2 cup of the beef broth and use a spatula to scrape the bottom of the pot thoroughly to remove any browned bits (deglazing) to prevent a 'Burn' error.
Add the remaining beef broth, tomato sauce, diced tomatoes, Worcestershire sauce, Italian seasoning, salt, pepper, and red pepper flakes.
Add the rinsed white rice to the pot and stir briefly to ensure the rice is submerged in the liquid.
Secure the Instant Pot lid and set the steam release valve to the Sealing position.
Select Manual or Pressure Cook on High for 5 minutes.
Once the cooking cycle is complete, allow the pressure to release naturally (NPR) for 10 minutes.
Carefully turn the steam release valve to the Venting position to release any remaining pressure.
Remove the lid, stir the soup to incorporate the rice evenly, and serve warm.