Can a new Apple device be exchanged in store?

I own an Apple device that is unopened and sealed, and was purchased at a store that is not Apple. Is it possible to exchange the product at an Apple Store for something equal to or greater than its value, by paying a bit extra to make up the difference in cost? Or is it impossible to do so, as it was not originally purchased through Apple?
Added (1). There is no proof of purchase, as it was a gift from a friend who already owned the product, so they gifted it to me. I don't know the name of the store it was purchased from, and I don't have the receipt.
Added (2). Also, the product I am referring to is an iPad mini 4, 32GB, and the reason that I would like to exchange it is because I found it to be quite small.

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