We investigate the THz emission characteristics of ferromagnetic/non-magnetic metallic heterostructures, focusing on thin Fe/Pt bilayers. In particular, we report on the impact of optimized crystal growth of the epitaxial Fe layers on the THz emission amplitude and spectral bandwidth. We demonstrate a 5 % enhancement of the emitted intensity, related to reduced spin scattering and higher interface transmission. Our work provides a pathway for devicing optimal spintronic THz emitters based on epitaxial Fe. It also highlights how THz emission measurements can be utilized to characterize the changes in out-of-equilibrium spin current dynamics in metallic heterostructures, driven by subtle structural refinement.