  Holography has provided valuable insights into the time evolution of strongly
coupled gauge theories in a fixed spacetime. However, this framework is
insufficient if this spacetime is dynamical. We present a scheme to evolve a
four-dimensional, strongly interacting gauge theory coupled to four-dimensional
dynamical gravity in the semiclassical regime. As in previous work, we use
holography to evolve the quantum gauge theory stress tensor, whereas the
four-dimensional metric evolves according to Einstein's equations coupled to
the expectation value of the stress tensor. The novelty of our approach is that
both the boundary and the bulk spacetimes are constructed dynamically, one time
step at a time. We focus on Friedmann-Lema\^itre-Robertson-Walker geometries
and evolve far-from-equilibrium initial states that lead to asymptotically
expanding, flat or collapsing Universes
