You probably just had condensation or other water in your exhaust system and it was just water vapor or steam blowing out of the exhaust which is fine. I think this is quite likely since you said it stopped pretty quickly.
If you have real white smoke, and it happens even when the car / exhaust is good and hot and you're sure there is no water in the exhaust, it could be trouble. If that is the case, first verify that it's really white and not gray smoke that maybe looked white in the lighting conditions. True white smoke is generally caused by burning either automatic transmission fluid or coolant. Since the NSX doesn't have ATF, it would be coolant, which is bad.
Gray or black smoke is from too much fuel and is normal on the NSX at full throttle, as the NSX runs rich at WOT. At part throttle it's a sign of some sort of trouble, such as a problem with an O2 sensor, MAP sensor, FPR, injector, air filter, etc.
You can easily smell the difference between coolant and fuel burning if you can get someone else to reproduce it while you're behind the car. Plain water of course doesn't smell like anything.