  Both the ${\cal N}=7$ superconformal quantum mechanics possessing the
exceptional $G(3)$ Lie superalgebra as dynamical symmetry and its associated
deformed oscillator with $G(3)$ as spectrum-generating superalgebra are
presented. This superconformal quantum mechanics, uniquely defined up to
similarity transformations, is obtained via the octonionically-induced
"quasi-nonassociative" method employed to derive the exceptional ${\cal N}=8$
$F(4)$ model. To construct the $G(3)$ theories, the covariant embedding of the
$7$-dimensional representation of the Lie algebra $g_2$ within the $8\times 8$
matrices spanning the $Cl(0,7)$ Clifford algebra is derived. The Hilbert space
of the $G(3)$ deformed oscillator is given by a $16$-ple of square-integrable
functions of a real space coordinate. The spectrum of the theory is computed.
