Prepare the carrots, celery, garlic, and onion.
Turn a 6-quart Instant Pot to the high sauté setting. Add the oil, and once it's hot, add the carrots, celery, garlic, onion, salt, and a large pinch of ground black pepper. Cook, stirring, until the vegetables are slightly softened, about 4 to 5 minutes.
Add the chicken and 8 cups of water. Cover the pot, select Manual, and set it to High pressure for 20 minutes.
When it beeps, turn to Quick Release. Once the valve drops, carefully remove the cover. Use tongs to remove the chicken from the pot and transfer it to a large bowl. Allow it to cool for several minutes. Using your hands or two forks, remove the skin and bones, and shred the meat into bite-sized pieces.
Switch the Instant Pot to the high Sauté setting and bring the soup to a boil. Once boiling, add the egg noodles and cook until al dente, about 4 to 5 minutes. DO NOT OVERCOOK THE NOODLES, as they will become soggy and absorb too much of the soup. Add the chicken back into the pot and stir. Adjust the salt to taste, if desired.
Turn off the heat, then divide the Chicken Noodle Soup into bowls and serve immediately.