We investigate the singularities of homogeneous cosmologies from the point of view of relational (and physically relevant) degrees of freedom of the gravitational field. These do not depend on absolute units of length and duration - thus they do not include the volume and extrinsic curvature. We find that the fully relational dynamical system remains well posed for all physical times, even at the point that would be described as the big bang when evolving present day data backwards in time.This result is achieved in two steps: (1) for solutions which are gravity-dominated near the singularity, we show that any extended physical clock (whose readings only depend on the relational degrees of freedom) will undergo an infinite number of ticks before reaching the big bang. The singularity is therefore pushed into the infinite physical past of any physical clock. (2) for solutions where a stiff matter component (e.g. a massless scalar field) dominates at the singularity, we show that the relational degrees of freedom reach the point that is described as the big bang in the dimensionful description of General Relativity (GR) at a finite physical time and evolve smoothly through it, because they are decoupled from the unphysical dimensional degrees of freedom, which are the only ones that turn singular. Describing the relational dynamics with the dimensionful language of GR makes the relational dynamics appear as two singular GR solutions connected at the hypersurface of the singularity in such a way that the relational degrees of freedom evolve continuously while the orientation of the spatial frame is inverted. Our analysis applies to all GR solutions which conform to the BKL conjecture, and is therefore relevant for a large class of cosmological models with inhomogeneity.