Some issues with a Wrangler

I have a 2016 Jeep Wrangler that when you first turn it on in the morning, mainly when it's cold outside, the Jeep will shake and have a vibration that you can hear and feel when you're in reverse and drive. It doesn't happen when you're in park or neutral. When you accelerate, the noise and vibration go away completely, and after driving it for some time, the noise and vibration are still there, but no where near as noticeable as they were when you first start up the vehicle.

I was in town with it earlier and it was doing exactly what I described above, but when I killed the engine and started it back up a couple minutes later, the noise and vibration were barely noticeable.

I've asked a couple other people about it and they said it could be the heat shields, but with these symptoms there is no way this is from a heat shield issue.

What do you guys think this issue could be? I'm gonna take it to a mechanic soon, but I just want some insight on what could be going on here.