Career mode starts with two trial laps after which the game provides you with suggested difficulty settings. This is then followed by a two lap race which you MUST win if you want to earn the PSN trophy/XBox achievement. If it seems you will NOT win the race (ie not in the lead before the final turn of lap 2 into the finish straight) then Pause and restart the race. You can keep doing this until you win* and unlock the "Proving Grounds" trophy.
[* Note: As illogical as it seems for a trial event that supposedly eases you into the game this first race can be very difficult to win as the default opponent AI setting is Medium. If like me you went for your best time in the two lap trial the opponent AI will reflect that. To keep the opponent AI in Easy giving you an almost foolproof chance of getting this trophy here's what you do: BEFORE you begin the career mode go to the options menu and manually set and save the AI difficulty to EASY and the driver handling to NOVICE and then deliberately get poor lap times in the evaluation trial. You then should have Easy AI opponents and win the race. IF YOU DON'T do that once you start the tutorial, you are locked at medium difficulty until after the race. You can readily change your driver capability and opponent AI difficulty after the trophy pops. Yes, totally counter-intuitive but that's how I finally won a race that was frustrating me no end, never getting better than 3rd place despite being ranked Experienced, and got the trophy.]
If, like me, you were unaware of this and you missed this trophy you will need to backup your current save file and then delete it from your console and start the game all over: redoing your controller setup, doing the trial laps and race (until you win it). You can then either continue or re-install your original save file depending on how far along in the Career you are.