engine chirp? normal?

280z/300zx

So I've noticed since owning my 370z that upon cold start there is a chirp noise from the engine. You can only hear if if you are standing near the front of the car. Once I get anywhere past the side mirrors I can't really hear it. After after driving it it goes away. For example, I get up in the morning start my car to go to work and hear the noise. When I get to work, 5 miles and 10min later, it's gone. Is this a normal thing for the VQ or do I need to take it in? Is there a fix I can do at home?

I've kind of noticed the same thing with the exhuast too. There is a slight vibration where the exhuast tips are but after warm up it's gone. These things are probably nothing to worry about but kind of annyoing for a 40k car. By the way, the car only has 350 miles on it. Not sure if it needs futher break in for these noises to stop or what