We consider the emergence of large-scale cosmological expansion in scalar-tensor theories of gravity. This is achieved by modelling sub-horizon regions of space-time as weak-field expansions around Minkowski space, and then subsequently joining many such regions together to create a statistically homogeneous and isotropic cosmology. We find that when the scalar field can be treated perturbatively, the cosmological behaviour that emerges is well modelled by the Friedmann solutions of the theory. When non-perturbative screening mechanisms occur this result no longer holds, and in the case of scalar fields subject to the chameleon mechanism we find significant deviations from the expected Friedmann behaviour. In particular, the screened mass no longer contributes to the Klein-Gordon equation, suppressing deviations from general relativistic behaviour.