You get a Quick Start by revving the engine at the start of a race and filling all 4 turbo bars - which essentially means tapping RT like crazy. Quite hard to do if you hold the controller normally, a bit easier if you tip the front of the controller up and tap RT with your index finger (or alternate between your index and middle finger).
Or; If you have a controller with turbo, this is the time to use it.
Do this 40 times to get: