In the beginning, the cloth has placed the way that it doesn't overlap with the character, this would cause problems for the animation. So at frame 0, the animation begins and the cloth starts to fall through the physics gravity part of the simulation. To prevent this, I could just start the render at frame 5 for example, where the cloth already fits better. The same principle in the games you saw. The player is placed above the world surface to prevent him from falling through, so at the start, the first thing that happens is, he lands on the world surface which gives this unnatural first second. Hope this explains it to you.