In this paper we present a framework in which the relational description of general relativity can be used to smoothly continue cosmological dynamical systems through the big bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor 𝜈. However, no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one, and measurable dynamical variables are, in fact, dimensionless ratios. This is manifest in the identification of a scaling symmetry or “dynamical similarity” in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exists unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat Friedmann-Lemaître-Robertson-Walker, Bianchi I, and Quiescent Bianchi IX cosmologies.