I tried attempting this "early" (before earning it in the Racer career) during online Hot Pursuit events. But that proved a bit difficult as there tends to be a lot of stuff to hit.
I also think that if you tap the brakes at all, it will void the achievement, as there was at least once I tried and thought I didn't hit anything but did tap the brakes to avoid a car or a wall and didn't get the achievement.
That said, once introduced in the Racer career, that event is perfect to earn the achievement. Several stretches of straight, open road.
The event which introduces the Turbo is Stampede Hot Pursuit, the 3rd event in East Gorge Canyon. I was about halfway through level 6 (Felon) level when I attempted the race. It may unlock sooner that level 6, but that's when I did the event.