If You're Not First, You're Last

The start of the track is actually the fallen gate where you knocked down the huge tire. The car usually gets stuck on the fallen gate, so you have to try a few times just to get the 'race' started off right. Other than that, as long as you accelerate through the straightaways, up hills, and take the shortcut, you should get it fairly easily. However, if you hit even one wall or miss one turn, it tends to screw you up and you'll have to try again.

Make sure you have the relic that Ellie gives you in an earlier side quest that'll enhance your car's boosting capabilities. It helps a LOT.