Super austenitic stainless steel (SASS) is a premium stainless steel (SS) variant which finds applications in challenging environments. One of the premium grades of SS that falls under the said category is AISI 904L. Autogenous activated flux tungsten inert gas (A-TIG) welding is an established technique for fabricating sound steel joints which offers various advantages. In this context, this research aims to identify an optimum set of input process parameters to effectively employ A-TIG welding to fabricate 10 mm thick joints of SASS AISI 904L plates by employing bead on plate welding trials. The input parameters varied for the trials are welding current, torch travel speed, and percentage of Argon gas present in a mixture of Argon and Helium – which is the shielding gas used, while the responses were the depth of weld penetration (DOP) and weld bead width (BW). For finalizing the combinations of input parameters and the run order of the welding trials, the design of experiments (DOE) was performed using central composite design (CCD) of response surface methodology (RSM). After performing the trials, the DOP and BW attained were measured and the data thus generated were analyzed to study the influence of varying input parameters on the two responses. Analysis of variance (ANOVA) was then performed to check the input parameter's level of significance. RSM's desirability approach was used for numerical optimization to attain maximum DOP and a moderate BW. A linear regression equation generated can be used to precisely predict DOP and BW for any random values of input parameters. The bead on plate trial's validation study displayed root mean squared error (RMSE) values of 0.328 and 0.653 for DOP and BW respectively, The RMSE values of DOP and BW of the joint fabricated with optimized parameters was 0 and 0.311 respectively.