When punching, do not start the punch by first moving the elbow or shoulder, or any other body part. Move the fist toward the target and then sequentially apply all the other necessary body parts so the fist is accelerated toward the target at its maximum speed and power.
Moving the fist first has another benefit; it helps prevent telegraphing the punch. If the fist moves first and moves directly at the opponent, the opponent will see a fist that appears to be getting larger. The eye detects movement quicker than it detects changes in size. This gives you a split second advantage before the opponent detects and reacts to the punch. A preliminary movement by the elbow, shoulder, or any other body part will warn the opponent of an attack. In addition, if the fist moves in a direction other than directly at the opponent, the movement will be detected quicker than a direct movement. Winging a punch give the opponent more time to react and evade or block the attack.
Of course, this means that you do not cock a punch. The punch just fires directly at the target from its present position. The punching action is similar to a jack-in-the-box toy; crank the toy, you hear the music, but you do not know then jack will pop up. When fighting, the opponent knows a punch will be coming at some point, but when it does, it should be a complete surprise.