Elastic properties from seismic data are important to determine subsurface hydrocarbon presence and have become increasingly important for detailed reservoir characterization that aids to derisk specific hydrocarbon prospects. Traditional techniques to extract elastic properties from seismic data typically use linear inversion of imaged products (migrated angle stacks). In this research, we attempt to get closer to Tarantola's visionary goal for full-wavefield inversion (FWI) by directly obtaining 3D elastic properties from seismic shot-gather data with limited well information. First, we present a realistic 2D synthetic example to show the need for elastic physics in a strongly elastic medium. Then, a 3D field example from deepwater West Africa is used to validate our workflow, which can be practically used in today's computing architecture. To enable reservoir characterization, we produce elastic products in a cascaded manner and run 3D elastic FWI up to 50 Hz. We demonstrate that reliable and high-resolution P-wave velocity can be retrieved in a strongly elastic setting (i.e., with a class 2 or 2P amplitude variation with offset response) in addition to higher-quality estimation of P-impedance and VP/VS ratio. These parameters can be directly used in interpretation, lithology, and fluid prediction.