How to know if my MacBook Air is not an used one?

The warranty date is predicated on the information Apple received upon its initial purchase — which apparently was the dealer from whom you purchased it. You can probably get Apple to correct it, but you must either call them on the phone or upload your original purchase receipt to Apple for verification.

Read About the purchase date or expiration date for your AppleCare agreement - Apple Support, and scroll down to "If your coverage expiration date is incorrect".

That would certainly explain the discrepancy in the dates. Warranty starts on the first day of original purchase. It would appear that your retailer purchased the unit from Apple on March 22nd. If this is an issue, you would need to contact the retailer to determine if return/refund is possible.

Confirm your warranty expiration date here: Check Your Service and Support Coverage - Apple Support

It's highly unlikely but you wouldn't want to miss out on warranty coverage if it were to expire by even one day. Apple is inflexible on that matter.

Where was the computer purchased? Was it an Apple authorized dealer?