The behavior of steel–concrete composite structures is significantly influenced by the efficiency of the shear connections that link the two materials. This research examines the performance of stud shear connectors, with an emphasis on analyzing the effect of different geometric design parameters. A computational model was created utilizing Python 3.13 to enable thorough digital monitoring of the influence of these parameters on the structural performance of composite connections. Developed within the ABAQUS framework, the model integrates geometric nonlinearity and the Concrete Damage Plasticity (CDP) approach to achieve detailed simulation of structural behavior. Essential design aspects, including stud diameter, stud height, head dimensions, and spacing in both longitudinal and transverse directions, were analyzed. The Python-based parametric model allows for easy modification of design parameters, ensuring efficiency and minimizing modeling errors. The significance of stud diameter changes was analyzed in accordance with Eurocode standards and previous studies. It was found that stud length has a reduced effect on structural performance, particularly when considering the concrete properties used in bridge construction, where compressive failure of the concrete zone is more critical at lower concrete strengths. Additional factors, such as stud head dimensions, were investigated but were found to have minimal effect on the behavior of steel–concrete composite connections. Longitudinal stud spacing emerged as a critical factor influencing structural performance, with optimal results achieved at a spacing of 13d. Spacings of 2d, 3d, and 4d demonstrated overlapping effects, leading to significant performance reductions, as indicated by comparisons of ultimate load and force–displacement responses. For transverse spacing, closer stud arrangements proved effective in reducing the likelihood of slip at the steel–concrete interface, enhancing composite action, and lowering stress concentrations. Additionally, reducing the transverse distance between studs allowed for the use of more shear connectors, increasing redundancy and enhancing performance, especially with grouped-stud connectors (GSCs).