As Newton's Laws states an object should be in rest or in constant velocity if no external force is applied. A man inside a stopped car cannot push the car as he is not giving any external force.But a man inside a bubble ball can make it move. What is the theory behind this? https://www.holleyweb.com/images/human_sized_hamster_ball_free_walking.jpg
The simple answer is that there is an external force, that of friction towards the ground. The man and the ball can thus change their velocity by using the friction provided by the ground, much in the same way we can walk by using the frictions on the ground.
An important follow up question, that the OP touches upon, is how the ball is actually made to move. Here again friction plays an important role by applying different amount of force in different direction a net movement can be achieved in any particular direction.
As an example, if the man decides to jump forward inside the ball, that will make the ball move forward. The reason is that when jumping forward the friction on the ground stops the ball from moving backwards, but when he lands, he transfers his momentum to the ball, which begins to roll.
By moving his weight around inside the bubble ball, and utilizing friction between his body and the ball, coupled with friction between the ball and the ground, the man can cause gravitational force to topple the ball and move it over the ground.
If the center of mass of the ball moves to one side of the ball, gravity will topple the ball toward its center of mass. Because the ball is in a uniform gravitational field, the ball's center of gravity is also its center of mass. By changing the ball's center of mass, the man changes its center of gravity. When the center of gravity changes, gravity moves the ball.