Conventional magnetic reconnection flows are envisioned to be driven from outside the current sheet, typically owing to large-scale MHD stresses. In the present work a two-dimensional electromagnetic particle-in-cell code is used to study a standard reconnection problem (the Newton Challenge) involving the transition from a moderately thick current sheet to a thinner sheet induced by a temporally limited, spatially varying, inflow of magnetic flux. The external forcing produces a small electron temperature anisotropy T$perp$/T$parallel$ $lesssim$ 1.1 and an embedded electron current layer on a scale below that of the ion inertia length. The reconnection involves a two-stage process with an initial fast (cEy/vAB0 ~ 0.1) phase followed by a second slow stage in which the O line structure of the magnetic island is established. For weak values of the flux inflow, these two processes occur on a common slow timescale. With an open geometry along the magnetic field line direction, the reconnection rate is increased and no island structure is formed; the plasma is simply expelled from the system. In the presence of an initial finite normal magnetic field component, the fast reconnection occurs only after the normal field is driven locally through zero and the electron stabilization effect is removed.