When the mechanical equilibrium of an object is disturbed, its velocity, acceleration, rate of change of acceleration and so on everything starts changing continuously. For a change of something the rate of change has to change and the same procedure gets repeated for rate of change. Thus what starts first is doubtful. In short, Newton’s laws cannot explain when does an object at rest start moving when force is applied on it. It only states that the object does not start moving instantaneously.