The investigation of atmospheric tsunamigenic acoustic and gravity wave (TAGW) dynamics, from the ocean surface to the thermosphere, is performed through the numerical computations of the 3D compressible nonlinear Navier-Stokes equations. Tsunami propagation is first simulated using a nonlinear shallow water model, which incorporates instantaneous or temporal evolutions of initial tsunami distributions (ITD). Ocean surface dynamics are then imposed as a boundary condition to excite TAGWs into the atmosphere from the ground level. We perform a case study of a large tsunami associated with the 2011 M9.1 Tohuku-Oki earthquake and parametric studies with simplified and demonstrative bathymetry and ITD. Our results demonstrate that TAGW propagation, controlled by the atmospheric state, can evolve nonlinearly and lead to wave self-acceleration effects and instabilities, followed by the excitation of secondary acoustic and gravity waves (SAGWs), spanning a broad frequency range. The variations of the ocean depth result in a change of tsunami characteristics and subsequent tilt of the TAGW packet, as the wave's intrinsic frequency spectrum is varied. In addition, focusing of tsunamis and their interactions with seamounts and islands may result in localized enhancements of TAGWs, which further indicates the crucial role of bathymetry variations. Along with SAGWs, leading long-period phases of the TAGW packet propagate ahead of the tsunami wavefront and thus can be observed prior to the tsunami arrival. Our modeling results suggest that TAGWs from large tsunamis can drive detectable and quantifiable perturbations in the upper atmosphere under a wide range of scenarios and uncover new challenges and opportunities for their observations.