We studied the variations of line of sight photospheric plasma flows during the formation phase of the penumbra around a pore in active region NOAA 11490. We used a high spatial, spectral, and temporal resolution data set acquired by the Interferometric BIdimensional Spectrometer operating at the NSO/Dunn Solar Telescope as well as data taken by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite (SDO/HMI). Before the penumbra formed we observed a redshift of the spectral line in the inner part of the annular zone surrounding the pore as well as a blueshift of material associated with opposite magnetic polarity farther away from the pore. We found that the onset of the classical Evershed flow occurs on a very short timescale (1 to 3 hr) while the penumbra is forming. During the same time interval we found changes in the magnetic field inclination in the penumbra, with the vertical field actually changing sign near the penumbral edge, while the total magnetic field showed a significant increase, about 400 G. To explain these and other observations related to the formation of the penumbra and the onset of the Evershed flow we propose a scenario in which the penumbra is formed by magnetic flux dragged down from the canopy surrounding the initial pore. The Evershed flow starts when the sinking magnetic field dips below the solar surface and magnetoconvection sets in.