  High temperature virial expansion is a powerful tool in equilibrium
statistical mechanics. In this letter we generalize the high temperature virial
expansion approach to treat far-from-equilibrium quench dynamics. As an
application of our framework, we study the dynamics of a Bose gas quenched from
non-interacting to unitarity, and we compare our theoretical results with
unexplained experimental results by the Cambridge group [Eigen et al., Nature
563, 221 (2018)]. We show that, during the quench dynamics, the momentum
distribution decreases for low-momentum part with $k<k^*$, and increases for
high-momentum part with $k>k^*$, where $k^*$ is a characteristic momentum scale
separating the low- and the high-momentum regimes. We determine the universal
value of $k^*\lambda$ that agrees perfectly with the experiment, with $\lambda$
being the thermal de Broglie wave length. We also find a jump of the half-way
relaxation time across $k^*\lambda$ and the non-monotonic behavior of energy
distribution, both of which agree with the experiment. Finally, we address the
issue whether the long-time steady state thermalizes or not, and we find that
this state does thermalize except for the very high momentum tail with
$k\lambda\gg 1$. Our framework can also be applied to quench dynamics in other
systems.
