Set Instant Pot to Sauté function and add oil. Add onion and cook until soft, 5 minutes. Stir in garlic and cook until fragrant, 1 minute, then add tomato paste, stirring to combine. Add ground beef and cook, breaking meat up with a wooden spoon, until no longer pink, 7 minutes. Drain fat, if necessary.
Return insert to Instant Pot and add broth, beans, tomatoes, chili powder, cumin, oregano, and cayenne. Season with salt and pepper. Lock lid and set to Pressure Cook on High for 14 minutes.