Computational discovery of organometallic catalysts that effectively catalyze nitrogen fixation is a difficult task. The complexity of the chemical reactions involved and the lack of understanding of natures enzyme catalysts raises the need for intricate computational models. In this study, we use a dataset of 91 experimentally verified ligands as starting population for a Genetic Algorithm (GA) and use this to discover molybdenum based nitrogen fixation catalyst in trigonal bipyramidal and octahedral configurations. Through evolutionary discovery with a semi-empirical quantum method driven GA and a density functional theory (DFT) based screening process, we find 3 promising catalyst candidates that are shown to effectively catalyze the first protonation step of the Schrock cycle. Synthetic accessibility (SA) scores are used to guide the GA towards reasonable ligands and the work features a description of the GA framework, including pre-screening of catalyst candidates that involves assignment of metal coordination atoms and catalyst stereoisomers. This research thus not only offers insights into the specific field of molybdenum-based catalysts for nitrogen fixation but also demonstrates the broader applicability and potential of genetic algorithms in the field of catalyst discovery and materials science.