  In this study, we prove that the quantum critical point in the ground state
of quantum many-body systems, can also govern the universal dynamical behavior
when the systems are driven far from equilibrium, which can be captured by the
evolution of the quantum geometry of the systems. By investigating quantum
quench dynamics in quadratic fermionic models, we prove that the quantum volume
of these systems typically grows linearly over time, with a growth velocity
demonstrating universal behavior: its first derivative over the control
parameter exhibits a discontinuity at the quantum critical point, with an
universal jump value that is independent of specific models, but is crucially
determined by the system dimension. This result reveals universal dynamical
properties of non-equilibrium quantum many-body systems
