Forza Motorsport

You get Car XP by completing sectors on track. The faster and cleaner the sector is, the higher its rating will be (between 1.0 and 10.0) and thus the more Car XP it rewards. Leaving the track limits (which will prompt you to rewind) and colliding with other vehicles will give you a 1.0 automatically which will not reward any Car XP.

So the fastest way to level cars is simply to drive cleanly and quickly. Pick cars you like driving & that fit your driving style. Rivals is a good way to grind this out since you can just lap on one car infinitely, though it's worth noting you also need a lot of multiplayer laps for the other achievements., so you can also pick a playlist your car is legal in and race online to work on those at the same time.

You will still need to play a lot, but this got faster and easier now that you can buy Car Points with credits. Upgrade it to the max of whatever class you're trying to race in before you start grinding.

I also recommend picking at least five cars from the same manufacturer for this so you can work on Brand Ambassador at the same time. Toyota is a good pick, but anything with at least five cars you can afford & want to drive is fine.