Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such inverse problems, in general, are ill-posed and nonconvex, especially in cases where the solutions exhibit shocks, heterogeneity, discontinuities, or large gradients. The proposed approach is proven efficient to obtain global minima responses in these cases. This approach is trained based on random sampled set of material properties and sampled trials around local minima, therefore, it requires a forward simulation can handle high heterogeneity, discontinuities and large gradients. High resolution Kurganov-Tadmor (KT) central finite volume method is used as forward wave propagation operator. Using the proposed framework, material properties of 2D media are quantified for several different situations. The results demonstrate the feasibility of the proposed method for estimating mechanical properties of materials with high accuracy using deep learning approaches.