We develop a Gabor-based Gaussian beam (GB) algorithm for representing two-dimensional (2-D) radiation from finite aperture distributions with short-pulse excitation in the time domain (TD). The work extends previous results using 2-D frequency-domain (FD) narrow-waisted Gaussian beams. The FD algorithm evolves from the rigorous Kirchhoff integration over the aperture distribution, which is then parameterized via the discrete Gabor basis and evaluated asymptotically for high frequencies to furnish the GB propagators to the observer. The TD results are obtained by Fourier inversion from the FD and yield pulsed beams (PB). We describe the resulting TD algorithm for several aperture distributions, ranging from simple linearly phased (linear delay) to arbitrary time delay profiles; the latter accommodate the important case of focusing TD aperture fields. For modulated pulses with Gaussian envelopes, we compute accurate closed form analytic solutions, which have been calibrated against numerical reference data. Our results confirm that the previously established utility of the Gabor-based narrow-waisted FD-GB algorithm for radiation from distributed apertures remains intact in the TD.