I would need a scrap car to try it with, but I can see how it is possible, based on the technique that allows a petit female rider to stand up a heavy motorcycle that has been dropped,
Not only was AtG strong, he was very tall, and very heavy. Those are important.
The key is that you DON’T really try to lift one side of the car. You end up doing so indirectly, but you will fail if you try to do it directly.
For this to work, the car must be on clean dry pavement, and you need the same for your feet, and high traction shoes.
Turn away from the car, squat down and grasp the car under the rocker panel, placing your back against the door.
Move your feet outward till your knees are only slightly bent, giving maximum mechanical advantage. Lift upward with your hands while using your legs to drive your back and shoulders into the car. As the car comes up, take quick baby steps backward to keep it moving while keeping your legs nearly straight.
You are essentially using your body as a wedge. But by angling your body against the car, you are using your weight to help roll the car, and not just muscle power.
The hard part is getting enough traction at the start. This is where being tall and heavy helps. The mass gives your feet more traction, and height allows your shoulders to apply the sideways force higher on the car, giving more leverage. If you are very strong, brut strength helps a lot, as you don’t need such an acute angle.
It also fails if the tires on the far side of the car slide.
If I were to pick a car to try this on, give me a mail jeep or a Suzuki Samuri.
By the way, this technique, applied at the bumper, also works to push a car. Since I have never owned a car with an automatic transmission, I have push started my cars many times. With practice, it is less bother than dragging out the jumper cables.