The deep drawing technique is an important metal forming processes, and it is rarely used in the Inconel 718 sheet. The main purpose of this study is to perform a deep drawing process using the Inconel 718 alloy. In this research article, the Inconel 718 alloy sheet of 1 mm thickness is drawn into sheet metal cups, and defects such as thinning, and earing are controlled using selected input parameters such as Blank Holding Force (BHF) Blank Diameter (BD), and Punch Nose Radius (Rpn). A Box Behnken design (BBD) is used to evaluate the effects of output parameters. The hybrid Deep Neural Network (DNN) is used to predict the experimental outcomes obtained from the deep drawing process. For deep drawing process blank holding force is favorable for both thinning and earing. The minimum thinning value obtained during experimentation is 0.033 mm. During experimentation less earing value is 2.47 mm. Hybrid Deep Neural Network based Sparrow Search Optimization (DNN-SSO) gives the prediction model, where the values are much closer to the experimented model than RSM and non-Hybrid DNN. The minimum thinning obtained in the prediction model such as RSM, SSO-DNN, and DNN are 0.030, 0.0304, and 0.023 mm. Likewise, the minimum earing obtained from the predictive model is 2.65, 2.49, and 2.51 mm respectively. The minimum error is found in the hybrid DNN and the average RMSE for thinning is 0.002 and earing is 0.0024. The regression coefficient of thinning and earing is 99% which proves the experimental outcomes matches with RSM validation.