Combine tomatillos, poblano pepper, jalapeno pepper, cilantro, lime juice, and garlic in a blender; blend until smooth. Set salsa verde aside.
Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Add olive oil, chicken, onion, oregano, and cumin; cook for 5 minutes. Add salsa verde, hominy, and chicken broth. Stir to combine.
Close and lock the lid. Select Manual function according to manufacturer's instructions; set timer for 20 minutes. Allow 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. Ladle posole into bowls.