  The finite parts of a large, locally interacting many-body system prepared
out-of-equilibrium eventually equilibrate. Characterising the underlying
mechanisms of this process and its timescales, however, is particularly hard as
it requires to decouple universal features from observable-specific ones.
Recently, new insight came by studying how certain symmetries of the dynamics
that are broken by the initial state are restored at the level of the reduced
state of a given subsystem. This provides a high level, observable-independent
probe. Until now this idea has been applied to the restoration of internal
symmetries, e.g. U(1) symmetries related to charge conservation. Here we show
that that the same logic can be applied to the restoration of space-time
symmetries, and hence can be used to characterise the relaxation of fully
generic systems. We illustrate this idea by considering the paradigmatic
example of "generic" many-body dynamics, i.e. a local random unitary circuit.
We show that, surprisingly, the restoration of translation symmetry in these
systems only happens on time-scales proportional to the subsystem's volume. In
fact, for large enough subsystems the time of symmetry restoration becomes
initial-state independent (as long as the latter breaks the symmetry at time
zero) and coincides with the thermalisation time. For intermediate subsystems,
however, one can observe the so-called "quantum Mpemba effect", where the state
of the system restores a symmetry faster if it is initially more asymmetric.
