How can I know if my iPhone 13 mini is new or used?

"The purchase date is older than I expected: [...]I know this model was discontinued on Sep. 2023. But I want to know if it has been activated or not (i.e. second-hand or not).[...]"

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You purchased a previously-owned device. It was purchased no the day it was purchased. When rung out at the register, the Serial Number is provided by the cashier, and it is then in Apple's data base. So, that is the date this was purchased by whomever.

Hello~ Your best course of action is to return that iPhone for at the very least you’re more than likely going to have a battery issue to contend with as it’s been sitting somewhere all this time. Get eBay involved if needed.

~Katana-San~

"Thank you for your reply!: I think I should contact to the seller. They sold it as new, but it wasn't. Hopefully I can get a refund"

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Purchasing a Used Apple Device:

Take this as a rule of thumb, knowing that this is all another reason to purchase a pricey used device from an AASP (Apple Authorized Service Provider) --to avoid scams and/or mishaps when buying or selling something. Go here to perform the return.

"The purchase date is older than I expected: Thank you for your reply!: I think I should contact to the seller. They sold it as new, but it wasn't. Hopefully I can get a refund”

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Contacting the seller sounds like the way to go about this.

Depends what the price is that you paid, and what was in the full description.

I just bought two "new, opened, never used, ex-display" iphone SE3s from ebay UK. They are physically unmarked, they have 100% original battery healtj, but obviously no Apple warranty, and in my case a USA model.

But hey at £158 each I am not complaining.