Turn on a multi-functional pressure cooker (such as Instant Pot(R)); select Saute function and adjust to medium. Cover the bottom of the pot with avocado oil. Cook and stir onion until soft, 4 to 5 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add rice to the pot and mix until coated with oil and lightly browned. Pour in chicken stock; stir any browned bits off the bottom of the pot. Add tomato sauce, salt, cumin, and cayenne pepper. Close and lock the lid. Seal the vent. Set timer for 7 minutes; allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir rice before serving.