You should replace all four tires at the same time
Replace individual tires as needed so long as they’re the same brand, model, and size as the rest of your tires. You can switch them out whenever. Just make sure to have them rotated at every other oil change to maximize their life.
Additionally, you don’t necessarily need to purchase a new tire if you puncture one. If the puncture damaged the sidewall or is greater than a quarter-inch in diameter, a mechanic can usually plug the hole. The patch will keep moisture out of the steel belts and restore your tire’s airtightness.