The single-point incremental forming process (SPIF) is one of the emerging manufacturing methods because of its flexibility in producing the desired complex shapes with higher formability at low-cost compared to traditional sheet forming methods. In this research work, we experimentally investigate the forming process to determine the influence of process parameters and their contribution to enhancing the formability without causing a fracture by combining the design of experiments (DOE), grey relational analysis (GRA), and statistical analysis of variance (ANOVA). The surface morphology and the energy dispersive X-ray spectroscopy (EDS) method are used to perform elemental analysis and examine the formed parts during three forming stages. The DOE procedure, a central composite design with a face-centered option, is devised for AA3003-H18 Al alloy sheet for modeling the real-time experiments. The response surface methodology (RSM) approach is adopted to optimize the forming parameters and recognize the optimal test conditions. The statistically developed model is found to have agree with the test measurements. The prediction model’s capability in R2 is computed as 0.8931, indicating that the fitted regression model adequately aligns with the estimated grey relational grade (GRG) data. Other statistical parameters, such as root mean square error (RMSE) and average absolute relative error (AARE), are estimated as 0.0196 and 2.78%, respectively, proving the proposed regression model’s overall closeness to the measured data. In addition, the prediction error range is identified as −0.05 to 0.05, which is significantly lower and the residual data are distributed normally in the design space with variance and mean of 3.3748 and −0.1232, respectively. ANOVA is performed to understand the adequacy of the proposed model and the influence of the input factors on the response variable. The model parameters, including step size, feed rate, interaction effect of tool radius and step size, favorably influence the response variable. The model terms X2 (0.020 and 11.30), X3 (0.018 and 12.16), and X1X2 (0.026 and 9.72) are significant in terms of p-value and F-value, respectively. The microstructural inspection shows that the thinning behavior tends to be higher as forming depth advances to its maximum; the deformation is uniform and homogeneous under the predefined test conditions.