In the Instant Pot, combine the chicken, onion, garlic, cilantro, hominy, and salsa verde. Add the chicken broth, salt, oregano, and 3 cups water.
Lock the lid into place and set the steam release valve to sealed. Select Manual or Pressure Cook and set the timer for 20 minutes on high.
When cooking is complete, allow the pressure to release naturally. Unlock and remove the lid.
Season the pozole with more salt, if necessary. Ladle into bowls and garnish with chopped onion, shredded cabbage, sliced radishes, and a squeeze of fresh lime juice. Serve with tostada shells or tortilla chips (if desired).