<p>Green hydrogen holds significant promise for a sustainable energy transition, but its production, transportation, and storage (PTS) technology investments are challenged by dual uncertainties: volatile market demand and the unpredictable timing of technology breakthroughs. This paper introduces a novel multi-regime stochastic dynamic optimization framework that integrates exogenous random stopping times to optimally guide technology investment decisions in the green hydrogen sector. Utilizing a dynamic stochastic optimal control formulation solved via Hamilton–Jacobi-Bellman equations, we rigorously capture the interplay between random technological advancements and fluctuating market conditions. Our numerical simulations demonstrate that the inherent unpredictable nature of PTS technology breakthroughs significantly amplifies market volatility and leads to non-linear investment trajectories. These findings underscore the need for adaptive investment strategies, robust risk management, and dynamic policy interventions that can mitigate such uncertainties. Unique to our work is the extension of single regime-switching models to accommodate multiple sequential breakthroughs, thus providing a more realistic and comprehensive decision-making tool for stakeholders. The insights derived not only contribute to the theoretical understanding of investment under dual uncertainties but also offer practical guidance for policymakers and industry practitioners, paving the way for further research in multi-period technology breakthroughs and sustainable energy investment frameworks.</p>