How to find the unboxing date of an Android device? Someone told me that he has opened a phone only 4 days ago, but by the look of it, it is not less than a month.

When trying to buy a used phone, is there any way to check how long this phone is in use? Or the date when this phone is turned on the first time? Or the time of unboxing? Or the time of the first usage?
You can simply go the Service menu of your phone and see the total call time which is very hard to reset. By that, you can assume how long it has been used.

As of Android 4.3 Jellybean, that is the best you can get.