The onset of the formation of structure in the early universe was marked by the monolithic collapse of smooth peaks in the initial density field. This process creates prompt rho ~ r^-1.5 density cusps of dark matter, which persist largely unaltered through the subsequent growth of dark matter halos around them. Consequently, in the standard collisionless dark matter paradigm, these prompt cusps are expected to be enormously abundant, and one resides at the center of every halo and subhalo. Prompt cusps present new opportunities to test the nature of dark matter. In annihilating dark matter models, the abundance of these features and the high density inside them greatly influence the intensity and morphology of the annihilation signal. For example, if the Galactic Center gamma-ray excess is due to annihilating dark matter, then a matching signal from unresolved prompt cusps should be detectable elsewhere. Moreover, the properties of prompt cusps are closely linked to details of the primordial density field. In warm dark matter models, prompt cusps are expected to be large enough to influence stellar motions within galaxies at detectable levels.