I've never heard of such a thing happening, and I'm kind of trying to wrack my brain as to what might be causing it. I've gotten a better vape quality in some tanks after the coil heats up a bit, but I am talking less vapor for the first few puffs, or just cooler vapor, I've never noticed increased harshness from it though.
Best of luck figuring it out! How many puffs does it take to reach "smooth" and what is your vape equipment? The answers to that MAY help (and I'm assuming it's at all times, not just when you put in a new coil?) Because a new coil does require breaking in and if you aren't priming it well, that (I am thinking? Maybe?) could cause harshness. IDK. If your coil has a ton of mass in it, it may require some puffs to get going more evenly but I'm still sort of wondering how that might cause the issue you describe.
Best of luck figuring it out!
Anna