Mine is the same way, its noisy as crap for about a minute, it is choked really high and sounds like the exhaust is leaking...I do think it has something to do with vvel, nothing else makes sense, once the rpms come down a bit it goes away. I have a header back exhaust(no cats).

I was thinking the same thing. Just bought a 40th Anniversary with 23k miles. And it almost sounds like an exhaust leak from where the headers meet the exhaust. I thought I was going crazy but my brother and a few friends noticed it too. Putting it up on a lift soon to check under there and find out for sure.

Why are people still wondering? Its exactly what I said it was. Many new cars do it, my mothers 2010 Forester XT does the same thing. I could be wrong but it might even mention it in the owners manual.

Warm Up and Response Time
 

Thanks for the information everyone it was very helpful. I guess I see what the purpose of the warm-up is for but I can't understand why they couldn't make it sound more appealing. I was taken back by how quite the car is in general compared to the 350s and G35s but keep in mind I bought it brand new with 12 miles on it. Now that is has been broken in it actually sounds louder but so does that awful warm-up. Yes, it goes away but it reminds me of the rattle that my stinking clutch makes.

At my 1,000 mi dealer inspection I mentioned the clutch and the guy heard it when he pulled it forward. It seems to do it in 1st gear at rolling speeds the most.....right after or while releasing the clutch. Dealer said it was normal.
I love Zs so I have a bit more tolerance but my 4,000 mi inspection is going to be painful because there are now 2 things I HATE about this car.

1) THEY COME WITH **** TIRES: Supposedly these are "performance tires," but after the first real storm I realized the Bridgestone Potenza RE050A tires are worthless in the rain!!! I couldn't go over 40 without feeling my life was in jeopardy while other cars were passing with ease. Looked up reviews and there are plenty of consumers with the same complaints. Also, many complain of the tread life being horrible around 16-17k mile tread life and after 60% tread they get slick. Think I'll stick with Hancooks but pissed the dealer didn't put more thought into an amazing car. Not sure if they will do anything but I am going to bring it up.

2) THE CLUTCH EMBARASSES ME WITH THE RATTLE: I refuse to drive an automatic sports car, DONT BELIEVE IN IN. Yes, this clutch is picky but they rattling makes the car sound cheap. Yes, S mode helps but I should be able to drive without it and I do just fine until the dreaded rolling in 1st mode ( parking lots, drive thrus)

1) There not all season tires. Sounds like you should have got a 4x4 truck. Then again a regret post. The Z is the ****. Who cares if they are passing you buy. Its raining anyways why do you need to be speeding for.

2) Learn how to drive your car.