Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function; if available, select "more" option. Add ground beef, salt, and pepper. Cook and stir beef until browned and crumbly, 5 to 7 minutes. Add onion and cook until starting to soften, 1 to 3 minutes more. Add olive oil and rice. Cook and stir until some grains start to turn golden brown, about 2 minutes. Stir in beans, tomatoes, broth, and taco seasoning.
Close and lock the lid. Select high pressure according to manufacturer's instructions; 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. Fluff burrito bowl filling with a fork and add cilantro.
Serve filling in tortillas with Mexican cheese blend. Garnish with fresh tomatoes, avocado, sour cream, and green onions.
