It's really bad customer service from the store, they can check when it was sent, when it was received and when you called. They should take responsibility for it. The iPhone you got is a DOA (Dead On Arrival)
Good thing you haven't switched it on or activated it, that also means it hasn't been used yet. Does the place where you bought it not have a physical store that you can come to?
If not, I would choose to return it and get my money back. The rules differ from country to country, but where I live, I have the right to return products bought online within 14 days, even if the product has been opened. It might be your solution, then you can buy it elsewhere. For example, in a physical store, where you can open the box together with the seller.
You can also try contacting Apple Support by phone. I don't know if they can do anything when it's bought elsewhere - but the product ultimately comes from them, so maybe they can help with something.
You can find your local Apple Support number here:
Contact Apple for support and service - Apple Support