During the game start you must select one car of the three initially available (as far as I remember), then after the tutorial you should go to Customize and select Color.
My first car had only the white color and it couldn't be changed at all, so if you are lucky, you'll be able to get the achievement with your first car.
Changing the color for my second car needed 5 gold currency, so don't waste all the ones you get when the game starts.