For quality assurance and in-service safety, sufficient characterization of the materials is essential during the development, manufacture, and processing of a material in any industrial setting. Evaluation of elastic coefficients, material microstructures, morphological features, and related mechanical properties are all part of the process of characterizing a material. Ultrasonic signals are sensitive to material properties such as wave speeds, attenuation, diffusion backscattering, microstructural variation, and elastic characteristics (e.g., elastic modulus, hardness, etc.). Ultrasonic computed tomography (USCT) is an emerging imaging method that can be implemented to obtain a quantitative estimation of material properties. In this study, a source estimation technique was initially proposed to obtain the source time function for accurate forward modeling by constructing a linear inverse problem for the unknown transducer modeling. Finally, a material characterization approach was proposed with accurate source estimation to extract wave speed distribution from an elastic material by employing a wave-based method, known as full waveform inversion (FWI). Systematic performance analysis of the proposed FWI model with accurate source estimation was assessed using experimental and synthetic data obtained from a 6061 aluminum sample. Overall, the proposed FWI technique has successfully reconstructed the wave speed distribution, exhibiting the potential of the proposed method of material characterization in various engineering applications.