My wife's 2012 does the same thing. Sits a week and sound like a bucket of bolts for a few seconds. I think it is the lifters involving the VVT. My friends 2015 is quiet on startup. We haven't had the head issue and when running after the rattle it's dead quiet so I don't sweat the noise.
2014 JKU, red, 2.5" AEV lift,6.4L VVT, 35" Duratrac's. 4.10, Gen Right bumpers, VR 8000 winch, Pro Rock 44.