Theoretical investigations predicted that high spatiotemporal resolution observations in the Sr I 4607 Å line must show a conspicuous scattering polarization pattern at the solar disk center, which encodes information on the unresolved magnetism of the intergranular photospheric plasma. Here we present a study of the impact of limited time resolution on the observability of such forward-scattering (disk-center) polarization signals. Our investigation is based on three-dimensional radiative transfer calculations in a time-dependent magnetoconvection model of the quiet solar photosphere, taking into account anisotropic radiation pumping and the Hanle effect. This type of radiative transfer simulation is computationally costly, which is why the time variation had not been investigated before for this spectral line. We compare our theoretical results with recent disk-center filter polarimetric observations in the Sr I 4607 Å line, showing that there is good agreement in the polarization patterns. We also show what we can expect to observe with the Visible Spectro-Polarimeter at the upcoming Daniel K. Inouye Solar Telescope.