I have forgot my AirPods purchase date what can i do?

Go to this web site: Check Your Service and Support Coverage - Apple Support - https://checkcoverage.apple.com/

It should have the date in the context of warranty information.

Or look on your receipt, or order history.

For items from the on-line store go to apple.com, scroll to the bottom, and click on Apple Store Account. --> https://www.apple.com/us/shttps://www.apple.com/us/shop/goto/account

For a physical Apple Store purchase you can try contacting the store where you purchased the phone and see if they still have a record of the purchase.

Viewing & Changing Orders - Shopping Help - Apple - https://www.apple.com/shop/help/viewing_changing_orders - "Once an item is shipped or picked up, Apple will create an invoice for your order. To view or print your invoice, go to your Order Listing(Opens in a new window) page and select an item to go to the order details. Then, select View Invoice at the top of your order details page to access your invoice. If you need help viewing or printing your invoice, speak with an Apple Specialist at 1‑800‑MY‑APPLE."

Apple recommends you "Keep your receipt after you buy an Apple device" - https://support.apple.com/HT202711

Contact the store where you purchased them.