Carea more about big prey than you, so try to run past anything bigger and meatier than you, then keep running. It won't take long to kill whatever it finds. That being said, I did see a Rex take a long while to kill 2 carbonenemy turtles
This is tge least threatening creature in the game once you hit lv 10. Craft a bow and some arrows, shoot it and kite. If it is gaining on you, run past a herbivore, it will lose aggro almost instantly. Keep shooting that sweet sweet early exp and possibly early metal tools.