The suppression of an ordered state is often discussed as a pathway to enhancing superconducting (SC) transition temperatures. Transition-metal dichalcogenides (TMDs), where both charge-densitywave (CDW) order and superconductivity arise from electron-phonon coupling, offer an ideal platform to study this interplay. We performed high-pressure single-crystal X-ray diffraction (XRD) and inelastic X-ray scattering (IXS) on 2H-TaSe2 and traced the evolution of its CDW superstructure and soft phonon mode over a broad temperature-pressure range. Our measurements show that the suppression of CDW order remains continuous down to low temperatures, demonstrating the persistence of a second-order phase transition, which is a necessary prerequisite for a CDW-related quantum-critical scenario. These findings refine the understanding of how CDW order collapses under pressure and how this behavior relates to the reported maximum superconducting transition temperature near 20 GPa. Overall, 2H-TaSe2 emerges as a controlled model system for investigating the interplay between CDW order, lattice dynamics, and superconductivity.