Place the whole chicken in the Instant Pot, breast side up. Add water, Adobo, and black pepper. Lock the lid, close the vent, and set the cooking time for 30 minutes at high pressure. Once cooking time is complete, allow pressure to release naturally (about 30 minutes).
While chicken cooks, place onions in a food processor and pulse until coarsely chopped. Add tomatoes, red bell pepper, cilantro, garlic, and capers, and pulse until combined (makes about 2 cups).
Transfer the chicken to a separate bowl (it may fall apart). Pass the broth through a fine mesh strainer and return to the Instant Pot.
Add sofrito, Sazón Goya, olives, and rice to the broth. Mix well. Lock the lid and cook at low pressure for 4 minutes. Allow the pressure to release naturally for 10 minutes, then quick-release the remaining pressure.
While the rice cooks, separate the chicken meat from the bones into bite-sized pieces. Discard the skin and bones.
Add chicken pieces to the pot mix well, and serve.