0_6917 The investigation of the mechanisms driving the stabilization of charge density waves (CDW) in low-dimensional crystals has garnered a great deal of attention from the ab initio community in recent years. In this contribution, we discuss the case of bulk MoS2 at low temperature (<10 K) and ultra-high hydrostatic pressure (~20-30 GPa) and argue that here a CDW transition can be explained as purely induced by the nonlocal part of the electron-electron interaction: i.e., this system is a candidate for being a real excitonic insulator. Firstly, we show that at the critical pressure, an exciton with finite center-of-mass momentum acquires negative energy in the absence of a corresponding softening of phonon modes. This leads to a purely electronic phase transition with the appearance of a CDW with antiferroelectric character. Secondly, we theoretically investigate the inelastic X-ray scattering spectra (IXS) of bulk MoS2 under pressure. We discuss the pressure dependence of the rich fine structure appearing in the resulting spectra including both lattice vibrations and neutral electronic excitations, in order to track the possible pathways of both excitonic and phononic instabilities towards the CDW phase transition.