In this paper we introduce SynaptoGen, a novel framework that aims to bridge the gap between genetic manipulations and neuronal network behavior by simulating synaptogenesis and guiding the development of neuronal networks capable of solving predetermined computational tasks. Drawing inspiration from recent advancements in the field, we propose SynaptoGen as a bio-plausible approach to modeling synaptogenesis through differentiable functions. To validate SynaptoGen, we conduct a preliminary experiment using reinforcement learning as a benchmark learning framework, demonstrating its effectiveness in generating neuronal networks capable of solving the OpenAI Gym's Cart Pole task, compared to carefully designed baselines. The results highlight the potential of SynaptoGen to inspire further advancements in neuroscience and computational modeling, while also acknowledging the need for incorporating more realistic genetic rules and synaptic conductances in future research. Overall, SynaptoGen represents a promising avenue for exploring the intersection of genetics, neuroscience, and artificial intelligence.