Sound velocity characterizes how the stiffness of matter changes as density increases. Nuclear many-body calculations and nuclear constraints indicate that matter is soft up to 1-2n0 (nuclear saturation density), while neutron star observations require stiff matter around 3-5n0 to pass the so-called two-solar mass constraint. This suggests that the QCD equation of state must have soft-to-stiff evolution in the interval of 2-5n0. Purely nuclear matter calculations typically lead to gentle stiffening to ~5n0.. We argue that the quark substructure of baryons is important even before baryons substantially overlap, leading to rapid stiffening and the sound velocity peak. These features are implemented in the Quark-Hadron-Crossover (QHC) equation of state (EOS). Using this EOS we study neutron star observables, in particular, gravitational waves in the post-merger phase, and quantify how large the impact of the sound velocity peak can be.