It can be possible in the following 2 cases:
Exactly at the start of the motion where the initial velocity is zero but the body is acted upon by a possible force.In the presence of a retarding force which brings the velocity of the body to zero with time.To provide a correction to the details of the question, dv/dt = 0 doesn't mean that either v=0 or t=0. It just implies that the rate of change of velocity is 0 i.e. the velocity is constant. I hope you agree with this.

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If we throw an object vertically upwards after reaching its maximum height it stops for a while when it stops its velocity is zero and acceleration acts vertically downwards as acceleration due to gravity