Your first shot at earning a gold medal comes at the second to last test during the first day of the Young Driver Tests. If you're playing with all assists on, this trophy will be a piece of cake. Follow the racing line, let the auto-brake kick in, and make sure you're leaning on the accelerator coming out of each turn. Make sure you hit each chevron location on the way through the test. Once you hit the straight, stay on the accelerator. When you begin getting close to the red stopping zone ahead, pull the right trigger to brake. You should stop towards the front of the stopping zone for the best time.
I don't know of the exact time to achieve a gold medal, but I first got a silver medal at 33.5 seconds, but tried again and got a gold medal at around 32.5 seconds. Regardless, you can easily retry the test if you didn't get a gold medal the first time to ensure you get the gold medal.