TBH you have no control whether you get a "new" device or a refurbished device, and in all honesty should not feel entitled to either. Apple will sort your problem under warranty, that's all that matters.
I had the "white spot" issue on my day one 10.5 iPad pro (week 21, may 2017), and did an Apple Care express replacement on it. I received a replacement device that was in a foam envelope inside a brown box. This device came with iOS 11 something and was week 46, November 2017. This device had a sub-par display, so I initiated another express replacement. The next replacement was in a white box inside a brown box. This was a week 21, may 2017 device and had iOS 10.3.2 installed (the version of iOS that shipped on the 10.5 from day one). This device is "perfect".
The fact this was in a white box and still had 10.3.2 on it leads me to believe it was a new device that had been packed in the "white box" and was directly allocated as replacement stock from new. Had it been refurbished, i'd have expected it to arrive with a newer iOS version.
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When it comes to replacement of a device, the new device will generally always be in a brown box. Even if the device is brand new. That’s their replacement packaging. Replacement units contain specific SKU, they can’t just pick a brand new device off the shelf and give you.
I've had an instance where I went through 4 or so replacement iPad Mini 2's within 2 days with issues that the Apple store staff could see, and they ordered me a brand new retail one as a replacement. They did all act like they were "doing me a favour", but it can happen