  Recent studies have demonstrated the possibility to uphold classical
determinism within gravitational singularities, showcasing the ability to
uniquely extend Einstein's equations across the singularity in certain
symmetry-reduced models. This extension can be achieved by allowing the
orientation of spatial hypersurfaces to dynamically change. Furthermore, a
crucial aspect of the analysis revolves around the formulation of the dynamical
equations in terms of physical degrees of freedom, demonstrating their
regularity at the singularity. Remarkably, singular behavior is found to be
confined solely to the gauge/unphysical degrees of freedom. This paper extends
these results to gravity coupled with Abelian and non-Abelian gauge fields in a
symmetry-reduced model (homogeneous anisotropic universe). Near the Big Bang,
the dynamics of the geometry and the gauge fields is reformulated in a way that
shows that determinism is preserved, assuming a change in orientation at the
singularity. The gauge fields are demonstrated to maintain their orientation
throughout the singularity, indicating that the predicted orientation change of
spatial hypersurfaces holds physical significance. This observation suggests
that an observer can discern the specific side of the Big Bang they inhabit.
