The dynamics of many-body systems spanning condensed matter, cosmology, and beyond are hypothesized to be universal when the systems cross continuous phase transitions. The universal dynamics are expected to satisfy a scaling symmetry of space and time with the crossing rate, inspired by the Kibble-Zurek mechanism. We test this symmetry based on Bose condensates in a shaken optical lattice. Shaking the lattice drives condensates across an effectively ferromagnetic quantum phase transition. After crossing the critical point, the condensates manifest delayed growth of spin fluctuations and develop antiferromagnetic spatial correlations resulting from the sub-Poisson distribution of the spacing between topological defects. The fluctuations and correlations are invariant in scaled space-time coordinates, in support of the scaling symmetry of quantum critical dynamics.