Using a two-color ultrafast surface deflection spectroscopy, we demonstrate the time-resolved observation of acoustic phonon wave packets emitted from a single buried GaAs quantum well. A longitudinal acoustic phonon pulse is generated at a preselected depth within a highly confined region ( $\ensuremath{\ge}10\mathrm{nm}$ thick) through the coherent nonequilibrium deformation potential which was previously unobserved in such structures. Subsequent detection with subpicosecond resolution at the surface resolves propagating high-wave-vector ballistic phonons and quasiballistic or ``snake'' phonons which subsequently merge into a quasidiffusive phonon pulse.