This article explains how to add AppleCare to your iPhone. You should be able to add AppleCare to your new iPhone within 60 days of purchase, as long as you keep your proof of purchase.
✅ How to add Applecare to iPhones 🔴
There are four ways to add AppleCare to your iPhone. You can do it from your iPhone, a web browser, over the phone, or by visiting an Apple Store.
If you add AppleCare coverage from your iPhone, you don't even have to dig for your receipt.
Open Settings on your iPhone. Go to General > About.