To prove the Newton's first law,
You can place a box on the floor. It will continue to remain in the state of rest unless, you apply some external force on it.
This will prove the Newton's First law.
To prove the Newton's second law,
By applying the force on the same box, the box will start moving.
The initial velocity of the box before the force is zero
After the force, the box velocity will become non-zero.
Thus, the change in the velocity of the box takes place with time under the action of force.
The change in the velocity with time is the acceleration.
Thus, acceleration of the box or rate of change of momentum of the box is directly proportional to the applied force.
This proves the Newton's second law.
To prove the Newton's third law,
When force is applied on the box, till the force does not cause any motion, there is an equal reaction force from the box is applied to the person ( who is applying the force on the box).
This proves the Newton's thrid law.