Set your Instant Pot to sauté mode. Add olive oil and cubed chicken. Cook until browned. Remove and set aside.
In the same pot, sauté onions, garlic, carrots, and celery until softened.
Pour in chicken broth, add thyme, rosemary, salt, and pepper. Stir well.
Return the cooked chicken to the pot. Add gnocchi. Close the Instant Pot lid and pressure cook on high for 5 minutes.
After cooking, stir in softened cream cheese until well combined.
Pour in half-and-half, and let the soup simmer on sauté mode until heated through.