In this paper, we present an optimization framework for green hydrogen (GH) production integrating photovoltaic generation, reverse-osmosis desalination, proton ex-change membrane electrolysis, and battery energy storage for continuous operation under solar intermittency. The study introduces a two-step ordinal optimization (OO) method to explore efficiently the large design space and identify subsystem sizes that minimize the levelized cost of hydrogen ($/kg), including production, storage, and transportation, at an average daily output of 60 tons of GH per day. First, the designs are evaluated using a simple, but computationally efficient model based on a two-week simulation. The evaluated designs are then scaled to a yearly operation and ranked by increasing hydrogen costs. Second, the top-S designs are re-evaluated using an accurate annual simulation model. OO theory predicts the number of top-S designs that need to be evaluated accurately to ensure that the optimum is included with a 95% alignment probability. We applied this framework to case studies for producing GH in Tunis and shipping it to Genoa in Italy and Hamburg in Germany, at costs of $3.91 and $6.40 per kg, respectively. The study leverages the potential of renewable energy (RE) production in Tunis and its proximity to Europe.