No, an object does not require a non-zero total force to move. According to Newton's first law of motion, an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity along a straight line unless acted upon by an external force.
This principle is often referred to as the law of inertia. Inertia is the tendency of an object to resist changes in its state of motion. An object will maintain its state of rest or motion unless acted upon by an external force.