I would not rely on the box cooler with that processor. Not a chance. It barely meets the requirements of the lower thermal design power units like the 3700x.
Keep in mind, the wraith coolers are cheap, budget units made for AMD by Cooler master, and they are just not very good. Will it WORK? Sure, it will "work". But it will suck AND it will be loud AND you will almost certainly not get the full benefit of any boost features out of your CPU because that cooler is just not capable enough for any kind of seriously demanding use of that CPU and anybody who HAS a 3900x and has no intention of pushing or punishing it, has wasted their money in buying it in the first place. If all you want to do is browse the interwebs and play solitaire, then sure, it's fine, but there was no point in getting that CPU in the first place.
I don't really understand why people buy a 700 dollar CPU and then quibble about getting a 50 dollar cooler. It's ridiculous.
If it were me, I wouldn't consider anything less than the Thermalright Macho rev.B or rev.C, or the Noctua NH-U14s or U12A, as the entry level requirements for that CPU. And go UP from there. But, that's just me. Seems reasonable to spend 50-70 dollars on a CPU cooler for a CPU that costs 700 bucks. But maybe I'm just being unrealistic.