Hydrogen is one of the most promising energy carriers in the quest for a more sustainable energy mix. In this paper, a model of the hydrogen supply chain (HSC) based on energy sources, production, storage, transportation, and market has been developed through a MILP formulation (Mixed Integer Linear Programming). Previous studies have shown that the start-up of the HSC deployment may be strongly penalized from an economic point of view. The objective of this work is to perform a sensitivity analysis to identify the major parameters (factors) and their interaction affecting an economic criterion, i.e., the total daily cost (TDC) (response), encompassing capital and operational expenditures. An adapted methodology for this SA is the design of experiments through the Factorial Design and Response Surface methods. Six key parameters are chosen (demand, capital change factor (CCF), storage and production capital costs (SCC, PCC), learning rate (LR), and unit production cost (UPC)). The demand is the factor that is by far the most significant parameter that strongly conditions the TDC optimization criterion, the second most significant parameter being the capital change factor. To a lesser extent, the other influencing factors are PCC and LR. The main interactions are found between demand, CCF, UPC, and SCC. The discussion has also shown that the calculation of UPC has to be improved taking into account the contribution of the fixed, electricity, and feedstock costs instead of being considered as a fixed parameter only depending on the size of the production unit. As any change that could occur relative to demand or CCF could strongly affect the response variable, more effort is also needed to find the more consistent way to model demand uncertainty in HSC design, especially since a long horizon time is considered for hydrogen deployment.