A lot of modern ECUs seem to pull back the power for the first thousand or so miles too. Pentastars are notorious for this, and at like 1200 miles you suddenly get a whole new car.
I've read a few times now that the 370Z seems to open up right around a thousand miles - might be something similar?
As for me, I baby the engine for 3-400 miles and then gradually push it harder and harder. I've redlined the Z a few times pulling some 0-60 passes now, but this is interspersed with casual around-town stop and go. I've done the same thing for about a dozen new cars now, with zero issues.
And yes, plan to have an oil change at 12-1500 miles just so you can check for metal content.