Okay.

Stop focusing on the treadmill.
The wheels are free-rolling. The movement of the wheels and the treadmill DON'T MATTER.

The engines light up, start generating thrust, and propel the plane FORWARD. During this movement, the wheels are spinning a trillion miles an hour in whatever direction you like -- IT'S IMMATERIAL!

As the thrust pushes the airframe forward atop those little spinning wheels WE DON'T CARE ABOUT, the air is moving across the wings faster and faster, until enough lift is generated, and the plane takes off -- at approximately the exact same distance down the treadmill-runway as it would on a concrete-runway.