The 3.7 has a distinct snarl to it when it starts. The 3.5 in the hybrid is a little more tame, although not mentioned by anyone here whether this discussion is a hybrid or regular engine we are talking about I suspect my old friend the VQ37 is the main suspect here. I have a Sport muffler on my coupe and it shakes the floor of my townhouse when started in the morning and my garage is climate controlled.
To those who are new to the brand the VQ37 uses what they call Variable Valve Event and Lift, it is similar to the old V-tech used by Honda but it works all the time instead of only over ~3K. Here is an older article that explains it better than I can.
VVEL | NISSAN | TECHNOLOGICAL DEVELOPMENT ACTIVITIES
Basically there are a lot more moving parts in there. The initial cold start is harsh sounding but it should not damage anything. The engine computers main goal is to reach operating temperature as quick as possible where it can better control the tailpipe emissions.
The noise should not persist longer than about 30 seconds but it may if the ambient temperature is really low.
I know they lack character. To me they sounds like a sewing machine, I want to know it's awake and ready to play.