  In large-$N_c$ conformal field theories with classical holographic duals,
inverse coupling constant corrections are obtained by considering
higher-derivative terms in the corresponding gravity theory. In this work, we
use type IIB supergravity and bottom-up Gauss-Bonnet gravity to study the
dynamics of boost-invariant Bjorken hydrodynamics at finite coupling. We
analyze the time-dependent decay properties of non-local observables (scalar
two-point functions and Wilson loops) probing the different models of Bjorken
flow and show that they can be expressed generically in terms of a few field
theory parameters. In addition, our computations provide an analytically
quantifiable probe of the coupling-dependent validity of hydrodynamics at early
times in a simple model of heavy-ion collisions, which is an observable closely
analogous to the hydrodynamization time of a quark-gluon plasma. We find that
to third order in the hydrodynamic expansion, the convergence of hydrodynamics
is improved and that generically, as expected from field theory considerations
and recent holographic results, the applicability of hydrodynamics is delayed
as the field theory coupling decreases.
