If I were to lay these down in my garage, can I park my car on top of them and move my car to workout without fear of damaging the tiles such as leaving permanent indention's?

You can drive a car over our 3/4" Shock Tiles. If you drive aggressively over them, there is a potential for the tiles to separate, but under normal driving, the tiles will hold up just fine. Outside of that, the only other thing you will need to look out for is the potential for tiles to degrade when they come in contact with oil. If you do have a car that does leak oil, we do suggest putting down a tarp where you will park your car.