  Thermalization is the dynamical process by which a many-body system evolves
toward a thermal equilibrium state that maximizes its entropy. In certain
cases, however, the establishment of thermal equilibrium is significantly
slowed down and a phenomenon of pre-thermalization can emerge. It describes the
initial relaxation toward a quasi-steady state after a perturbation. While
having similar properties to their thermal counterparts, pre-thermal states
exhibit a partial memory of initial conditions. Here, we observe the dynamical
formation of a pre-thermal state in a non-equilibrium, two-dimensional (2D)
fluid of light after an interaction quench. Direct measurements of the fluid's
first-order correlation function reveal the spontaneous emergence of long-range
algebraic correlations spreading within a light-cone, providing a clear
signature of a quasi steady-state strongly similar to a 2D thermal superfluid.
Detailed experimental characterization of the algebraic order is presented and
a partial memory of the initial conditions is demonstrated, in agreement with
recent theoretical predictions. Furthermore, by a controlled increase of the
fluid fluctuations, we unveil a cross-over from algebraic to short-range
(exponential) correlations, analogous to the celebrated Kosterlitz-Thouless
transition observed at thermal equilibrium. These results suggest the existence
of non-equilibrium precursors for thermodynamic phase transitions.
