Gravity waves play a crucial role in atmospheric dynamics. They are a major source of turbulence, which in turn has a huge impact on the vertical flux of momentum in the atmosphere. Despite their importance, the exact mechanisms by which gravity waves are generated and later promote turbulence transition are still largely unexplored. Here we propose a novel non-linear numerical framework to study the generation of gravity waves, and turbulence transition. We consider a Cartesian domain, with a steady mean shear, and as a model of the precursor of gravity waves we propose a spatio-temporal stochastic forcing. Using Bayesian optimization we aim to identify the distribution of the forcing that maximizes transition. To manage the high computational demands, we extend a pseudo-spectral GPU-based numerical code tailored for this purpose. Our goal is to uncover the physical mechanisms that lead to the most efficient transition, thus contributing to both fundamental turbulence theory and its practical application in atmospheric modeling.