We have simulated a Galactic population of young pulsars and compared with the Fermi LAT sample, constraining the birth properties, beaming and evolution of these spin-powered objects. Using quantitative tests of agreement with the distributions of observed spin and pulse properties, we find that short birth periods P0~ 50 ms and γ-ray beams arising in the outer magnetosphere, dominated by a single pole, are strongly preferred. The modeled relative numbers of radio-detected and radio-quiet objects agrees well with the data. Although the sample is local, extrapolation to the full Galaxy implies a γ-ray pulsar birthrate 1/(59 yr). This is shown to be in good agreement with the estimated Galactic core collapse rate and with the local density of OB star progenitors. We give predictions for the numbers of expected young pulsar detections if Fermi LAT observations continue 10 years. In contrast to the potentially significant contribution of unresolved millisecond pulsars, we find that young pulsars should contribute little to the Galactic γ-ray background.