As the global shift towards renewable energy accelerates, achieving stability in power systems is crucial. Hydropower accounts for approximately 17% of energy produced worldwide, and with its capacity for active and reactive power regulation, is well-suited to provide necessary ancillary services. However, as demand for these services rises, hydropower systems must adapt to handle rapid dynamic changes and off-design conditions. Fatigue damage in hydraulic machines, driven by fluctuating loads and varying mechanical stresses, is especially prominent during the transient start-up of the machine. In this study, we introduce a data-driven approach to identify transient start-up trajectories that minimize fatigue damage. We optimize the trajectory by leveraging a machine learning model, trained on experimental stress data of reduced-scale model turbines. Numerical and experimental results confirm that our optimized trajectory significantly reduces start-up damage, representing a meaningful advancement in hydropower operations, maintenance, and the safe transition to higher operational flexibility.