This is possible because an electric field is set up in the circuit as soon as it is closed, almost with speed of light. This causes a local electron drift at every point in the circuit. Establishment of a current does not require individual electrons to move from one end of the conductor to the other. Each free electron in the conductor accelerates due to the effect of the electric field until it collides with a positive ion of the metal and loses its drift speed. The electrons go through a continuous cycle of collision and successive loosing of drift speed until an average drift speed is reached.