Season pork with salt and pepper. Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Add garlic and olive oil; cook for 3 minutes. Add pork and cook until browned, about 2 minutes on each side. Add tomatoes, peppers, parsley, thyme leaves, and bay leaves; close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 45 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Discard bay leaves, and shred pork with 2 forks.