  Within the non-equilibrium Green's function (NEGF) formalism, the Generalized
Kadanoff-Baym Ansatz (GKBA) has stood out as a computationally cheap method to
investigate the dynamics of interacting quantum systems driven out of
equilibrium. Current implementations of the NEGF--GKBA, however, suffer from a
drawback: real-time simulations require {\em noncorrelated} states as initial
states. Consequently, initial correlations must be built up through an
adiabatic switching of the interaction before turning on any external field, a
procedure that can be numerically highly expensive. In this work, we extend the
NEGF--GKBA to allow for {\em correlated} states as initial states. Our scheme
makes it possible to efficiently separate the calculation of the initial state
from the real-time simulation, thus paving the way for enlarging the class of
systems and external drivings accessible by the already successful NEGF--GKBA.
We demonstrate the accuracy of the method and its improved performance in a
model donor-acceptor dyad driven out of equilibrium by an external laser pulse.
