If I don’t have the receipt but have the box and AirPods case, can I get a replacement?

Apple may ask you for proof of purchase if you are seeking warranty replacement or service for your AirPods:

Please put your product's sales receipt, and if applicable, AppleCare Proof of Coverage document in a safe place. You may be asked to provide a copy of these if there is any question as to your product's eligibility for service coverage under the warranty or AppleCare service contract. When seeking service, Apple may request that you submit the original sales receipt of your product to verify eligibility for warranty service, even if you have already registered your product. Your warranty is the same whether or not you register.