Choose Quick Race (or go into any mode where you'll be completing a full race). If you've chosen Quick Race, you can change the camera settings to Cockpit Cam on the Race Settings menu. If you're in a different mode, go to the Pause Menu while you're still in the garage. You'll be able to change your camera view from this menu. Just make sure that you are in Cockpit view before the race begins.
Once the race begins, you can finish in any position. The trophy will unlock at the end of the race as long as you finish it successfully (if you disqualify, the trophy may not unlock, as you did not fully complete the race).