We report evidence for a 1.0-THz self-starting mirrorless acoustic phonon parametric oscillator (MAPPO) produced from acousto-optic phase-conjugate degenerate four-wave (D4WM) mixing in a THz laser-pumped silicon doping superlattice (DSL). The DSL was grown by molecular beam epitaxy on a (100) boron-doped silicon substrate. A superconducting NbTiN subwavelength grating was used to couple the THz laser radiation into the DSL. Superconducting granular aluminum bolometric detection, coupled with Si:B piezophonon spectroscopy, revealed excitation of THz coherent compressional and shear waves, along the ⟨111⟩ direction only. The Bragg scattering condition for distributed feedback, and the energy conservation requirement for the D4WM process, were both verified. A THz MAPPO could provide a test bed for studies of nonclassical acoustic phonon fields.