Horizon Origins is a 5 part story in which you re-live the feeling of previous Horizon Games.
To get 3 stars in a chapter you need to complete the last race of the chapter in a specific time.
Since you don't need to get any checkpoints, you can straight go to the finish line.
Here's how I did the 3 stars:
Chapter 1: AMG ONE: I stuck to the road and managed to get 3 stars with barely a second left. If you make any errors you'd need to restart. Since there are many hills on the way to the goal it might be hard to cut through the landscape. It's a tough one.
Chapter 2: VW Corroda: Open the Map and check the goal. I instantly cut through the landscape at the start so I don't need to go the long way around to get to the road. Once you hit the road again you can race the target without any sharp turns to get a good time, as to be seen here:
https://imgur.com/iktSaZEChapter 3: Lambo Huracán: Cut the corners through the landscape and you should get to the destination with many time left
Chapter 4: 2014 Ford Rockstar Truck: Do not follow the suggested racing line, just go instantly left over the dunes and straight to the goal; you'll safe a load of time. Just be careful, right before the end is a hill.
Like This:
https://imgur.com/a/mwRqp2SChapter 5: McLaren Senna: Same with the lambo, cut corners that'd slow you down through the landscape. Just watch the trees!