It’s definitely possible to propel your body using muscle to move towards the ground quicker than gravity.
But is it possible to squat quicker than gravity?
Assuming squatting from your knees and not you bending down from your back like a lever, and that you’re not gripping the ground with your feet and pulling your self down.
If you dropped a basketball from the same height as your head,
would it be possible to squat below the basket ball before the basket ball hit the ground?