BUILD FLAVOR: Heat oil in instant pot on sauté' until shimmering. Add onion and cook until softened, about 5 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Stir in water, carrots, celery, and coconut amino, scraping up any browned bits. Season chicken with salt and pepper and place, breast side up, in pot.
HIGH PRESSURE FOR 20 MINUTES: Lock instant pot lid in place and bring to high pressure over medium-high heat. As soon as pot reaches high pressure, cook for 20 minutes.
QUICK RELEASE PRESSURE: Quick release pressure, then carefully remove lid, allowing steam to escape away from you.
BEFORE SERVING: Transfer chicken to cutting board, let cool slightly, then shred meat into bite-size pieces, discarding skin and bones. Meanwhile, using large spoon, skim excess fat from surface of soup. Bring soup to boil, stir in noodles, and cook until tender, about 5 minutes. Stir in shredded chicken and parsley, season with salt and pepper to taste, and serve.