The European Union is committed to a 55% reduction in greenhouse gas emissions by 2030, as outlined in the Green Deal and Climate Law initiatives. In response to geopolitical events, the RePowerEU initiative aims to enhance energy self-sufficiency, reduce reliance on Russian natural gas, and promote hydrogen utilization. Hydrogen valleys, localized ecosystems integrating various hydrogen supply chain elements, play a key role in this transition, particularly benefiting isolated regions like islands. This manuscript focuses on optimizing a Centralized Green Hydrogen Production Facility (CGHPF) on the island of Crete. A mixed-integer linear programming framework is proposed to optimize the CGHPF, considering factors such as land area, wind and solar potential, costs, and efficiency. Additionally, an in-depth sensitivity analysis is conducted to explore the impact of key factors on the economic feasibility of hydrogen investments. The findings suggest that hydrogen can be sold in Crete at prices as low as 3.5 EUR/kg. Specifically, it was found in the base scenario that, selling hydrogen at 3.5 EUR/kg, the net profit of the investment could be as high as EUR 6.19 million, while the capacity of the solar and wind installation supplying the grid hydrogen facility would be 23.51 MW and 52.97 MW, respectively. It is noted that the high profitability is justified by the extraordinary renewable potential of Crete. Finally, based on our study, a policy recommendation to allow a maximum of 20% direct penetration of renewable sources of green hydrogen facilities into the grid is suggested to encourage and accelerate green hydrogen expansion.