How to check if a new MacBook Air M4 is refurbished?

You can enter the serial number here to see if the device has warranty coverage:

View Coverage - AppleCare & Warranty

A real Apple refurb has a one-year warranty that starts when Apple ships it. If the check shows no coverage, it is not an Apple refurb.

In decades past, Apple computers that were factory refurbed were give a special serial number starting with R or RM. This is the tag on an eMac we bought directly from Apple in 2006:

They have not used that system in ages

There are order number codes in iPhones and iPads that denote a factory refurb but I have never seen it used for computers.

As MartinR wisely advices, you cannot buy a proper Apple refurb from other than Apple online. I recommend you return yours.

Your sales order/receipt should indicate new vs. refurbished. And AFIAK only Apple itself sells "Certified Refurbished" Macs, and they only sell them online.

If you are suspicious that the retailer sold you a refurbished MBAir but told you it was new, return it and get your money back.

I agree with the advice to return that Mac for a full cash refund, if for no other reason that the seller is being disingenuous at best by describing it as "refurbished". That Mac is used and should be resold as such. Even if it had been refurbished, selling it again makes it a used Mac.