Recently theorized hybrid II-IV-N{_2} / III-N heterostructures, based on current commercialized (In,Ga)N devices, are predicted to significantly advance the design space of highly efficient optoelectronics in the visible spectrum, yet there are few epitaxial studies of II-IV-N{_2} materials. In this work, we present heteroepitaxial ZnGeN{_2} grown on GaN buffers and AlN templates. We demonstrate that a GaN nucleating surface is crucial for increasing the ZnGeN{_2} crystallization rate to combat Zn desorption, extending the stoichiometric growth window from 215 {degree}C on AlN to 500 {degree}C on GaN buffers. Structural characterization reveals well crystallized films with threading dislocations extending from the GaN buffer. These films have a critical thickness for relaxation of 20 nm - 25 nm as determined by reflection high energy electron diffraction (RHEED) and cross-sectional scanning electron microscopy (SEM). The films exhibit a cation-disordered wurtzite structure, with lattice constants a = 3.216 {AA} {pm} 0.004 {AA} and c = 5.215 {AA} {pm} 0.005 {AA} determined by RHEED and X-ray diffraction (XRD). This work demonstrates a significant step towards the development of hybrid ZnGeN{_2}-GaN integrated devices.