I know this is an old thread, but I just wanted to let you know, I purchased a brand new GV60, and the hud is blurry. New from the lot with only 120 miles....
I'm very disappointed in the quality of fingerprint unlock, face unlock in low light conditions, and the blurry ass hud. Genesis/hyundai should be embarassed.
More than likely, the windshield has been replaced with
aftermarket. It is not unheard off for cars sold as brand new to have repairs and replacement done to it prior to sale to first owner. Dealership could have been hit with hail and a bunch of cars received damaged, or an individual car could have been hit with rock/stone on a test drive. At lot could happen in 120 miles + how ever long the car has been on the lot.
If the HUD was blurry, you should've refused delivery until dealer rectify the situation. If I suspected windshield problem, I would've checked the glass mfr code/label. There is one printed on every windshield, which would've indicated whether it is genuine OEM or
aftermarket windshield. Below is what a genuine Genesis glass label would look like. I took this pic of my OEM glass before it was replaced.
Regarding calibration after windshield replacement, it is primarily for ADAS, which is for the forward looking camera used by systems like lane keep assist and collision avoidance brake assist. It is only required if your car has such system. You can tell if your windshield block include something that looks like this:

Even then, if the replacement glass is of good quality and matches OEM glass contour closely, ADAS recalibration may not be necessary. Our '21 6MT G70 Sport has that forward facing camera but the company that did our replacement glass assured us ADAS calib was not required. We went for a test drive, and sure enough, lane keep assist worked perfectly and kept the car centered as well as prior to windshield replacement. That said, this is not always the case with other brands of generic replacement glass, so you need to make sure ADAS calib is included in your insurance quote, in case it is needed, before agreeing to the repair.
HUD is a whole 'nother animal. Not only is the glass contour important, so is the coating and construction of the glass laminate. The company that did my windshield replacement told me that if mine had HUD, he would've recommended I got with my insurance company to request for OEM glass. Other autoglass companies I talked to told me the same thing.