We use angle-resolved photoemission to map the Fermi surface and quasiparticle dispersion of bulk-like thin films of SrMoO$_3$ grown by pulsed laser deposition. The electronic self-energy deduced from our data reveals weak to moderate correlations in SrMoO$_3$, consistent with our observation of well-defined electronic states over the entire occupied band width. We further introduce spectral function calculations that combine dynamical mean-field theory with an unfolding procedure of density functional calculations and demonstrate good agreement of this approach with our experiments.