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Submarine groundwater discharges (SGD) are an important source of freshwater to coastal bays and estuaries in arid and semi-arid regions. Understanding groundwater flows to these ecologically sensitive bodies is important for coastal environmental sustainability. A management-oriented mathematical model capable of simulating the flow of groundwater into a coastal bay (i.e., submarine groundwater discharge) is developed here using the principles of quasi-steady-state flow and the existence of a sharp interface between the freshwater and the saltwater portions of the aquifer. The model is applied to the Baffin Bay in South Texas, a hypersaline coastal body with no major river discharges. Two global sensitivity approaches (the one-at-a time design; OAT) and the grid-based Monte Carlo sensitivity index are used to identify critical model inputs. The sensitivity of the model inputs to the Nash-Sutcliffe Efficiency (NSE) criterion is calculated making use of synoptic observed SGD measurements made over a period of one tidal cycle. The results of the study indicate that global sensitivity analysis methods are particularly sensitive to the number of model realizations. The ability of these techniques to screen out insensitive model inputs increased with increasing number of realizations. The variability in the identified inputs was more prominent with the OAT sensitivity methods than Monte Carlo-based techniques. In general, the aquifer properties (hydraulic conductivity and aquifer thickness) as well as fluid properties (seawater and fresh water densities) along with the antecedent SGD was noted to be the most sensitive parameters. This result indicates that the implementation of sharp-front coastal-aquifer models can be improved through better hydrogeologic characterization and measuring temperature and salinity data to improve density estimation. The global sensitivity methods also help identify reasonable values for model inputs which can serve as a starting point for advanced calibrations. The results, however, indicated that the model is likely over-parameterized with different input sets yielding similar NSE estimates. Based on these initial parameter estimates, the model was able to capture the general trend in the observed SGD but could not capture the dynamic associated with high water levels in the bay. Pre-calibration global sensitivity analysis is recommended in similar applications as it not only provides insights into future data collection efforts but can also help assess the likely success of model calibration. However, given the variability among the techniques, it is suggested that multiple global sensitivity methods be utilized.