Hydrogen production by electrolysis has gained considerable interest as a sustainable fuel source for transportation and a renewable energy carrier. The attractiveness of hydrogen production by this process is influenced by the emission-free chemical cycle and reaction characteristics of the technology, making the hydrogen production process environmentally sustainable. However, hydrogen prices are strongly dependent on electricity prices. Water electrolysis using a polymer membrane electrolyzer (PEM) is one of the most efficient ways to produce green hydrogen. Within the article, the focus was on analyzing several aspects of the electrolysis system powered by renewable energy: the availability of solar and wind resources in Poland and the annual energy demand. Available data from the Geographic Information System (GIS) on existing solar and wind resources across the country, among others, were collected and combined with capacity factors and capacities of photovoltaics, wind turbines, and an electrolyzer to determine the amount of hydrogen that can be produced from renewable sources. Part of the data for the analysis was taken from actual data of an existing test bed integrating a PEM electrolyzer and PV panel. These analyses helped define the challenges and opportunities regarding hydrogen's contribution to Poland's future energy economy.