Seismic Full Waveform Inversion has clearly demonstrated its efficiency in providing accurate quantitative information about the subsurface. Its implementation strongly depends on the resolution of the forward problem which is performed repeatedly in an iterative inversion process. In this work, we perform seismic FWI when the forward problem is solved with a face-based discontinuous finite element method. Discontinuous finite elements are particularly efficient for solving wave equations in heterogeneous media since with the hp-adaptivity feature, they not only can handle the topography of the propagation domain but also resist numerical pollution, which can be important in large-scale computations. Herein, we consider a Hybridizable Discontinuous Galerkin method based upon a mixed formulation of the problem coupled with static condensation. The computational burden mostly comes from the resolution of the global discrete problem whose size is proportional to only the degrees of freedom of the mesh skeleton. We work with the elastic wave equation in the frequency domain. We consider two different mixed formulations, the so-called strain-stress, and stress-strain formulations. This first one is widely used while the second one allows us to easily consider varying parameters inside the cells of the mesh. The HDG approximation of the elastic wave is the first step in the design of the FWI process. The second and critical step consists in deriving the adjoint state in the same approximation framework. This turns out not to be an obvious task and thus deserves some attention. We illustrate the numerical performances of the HDG-based FWI with time-harmonic elastic wave equations on two and three-dimensional test cases.