Add the olive oil to an Instant Pot set to sauté mode and heat until shimmering, approximately 3 minutes.
Add the onion, celery, and carrot to the pot and cook until softened. Stir in the garlic and cook for 1 minute longer.
Add water, the vegetable packet, and broth from the soup mix to the pot and stir.
Place the chicken in the pot and put the lid on.
Lock the lid in place and cook at high pressure for 10 minutes.
Turn off the heat and manually release the steam.
Carefully remove the lid from the pot and transfer the chicken to a cutting board.
Using two forks, shred the chicken into bite-sized pieces and return to the pot.
Turn the Instant Pot back to sauté mode and bring the soup to a boil.
Add the noodles to the soup and cook for 8 minutes or until the noodles are tender.
Season with salt and pepper, to taste. Serve immediately.