Drive up to the first checkpoint and slow down. Behind the boulders is a short patch of sand where you can drive onto the closed road. This of course is the "wrong way" and if you plan to go through it, you will be faster but not complete the lap. You will not win unless you do the following. Drive up to the end of the road, just past the "Dunniel" (or something similar) sign, where you get your checkpoint information and select "Replace Car" (default is KEYPAD 0). The goal is now just a couple inches away. You must to do this five times. By doing so, you can finish the race in a little less than six minutes. Note: Make sure you do not crash on the closed road as the "Replace Car" might not work there, or will place you back to the first checkpoint.
If you have a steering wheel, map it immediately. Gun it all the way on the first lap. Just get in the first place position by the finishing straight. You can now go safely to the finish line. On the big banked corner at the end, go very close to the wall as you will lose less speed.
Switch to manual gear ( PC default is M) just after you get past the stuck car. The gear then should switch to second , You would see the number "2" in the square in the middle of your speedometer. Remain in second gear until the end of the race. Slow down before turns (either release the key or brake before sharp turns). You still need tons of practice and must know the track in order to finish first. Also, if you are not at least fifth place after the first lap and at least third place after the second lap, start over. This will save plenty of time.