Over the last few decades, Instrumented Indentation Test (IIT) has evolved into a versatile and convenient method for assessing the mechanical properties of metals. Unlike conventional hardness tests, IIT allows for incremental control of the indenter based on depth or force, enabling the measurement of not only hardness but also tensile properties, fracture toughness, and welding residual stress. Two crucial measures in IIT are the reaction force (F) exerted by the tested material on the indenter and the depth of the indenter (D). Evaluation of the mentioned properties from F–D curves typically involves complex analytical formulas that restricts the application of IIT to a limited group of materials. Moreover, for soft materials, such as austenitic stainless steel SS304L, with excessive pile-up/sink-in behaviors, conducting IIT becomes challenging due to improper evaluation of the imprint depth. In this work, we propose a systematic procedure for replacing complex analytical evaluations of IIT and expensive physical measurements. The proposed approach is based on the well-known potential of Neural Networks (NN) for data-driven modeling. We carried out physical IIT and tensile tests on samples prepared from SS304L. In addition, we generated multiple configurations of material properties and simulated the corresponding number of IITs using Finite Element Method (FEM). The information provided by the physical tests and simulated data from FEM are integrated into an NN, to produce a parametric mapping that can predict the parameters of a constitutive model based on any given F–D curve. Our physical and numerical experiments successfully demonstrate the potential of the proposed approach.