  We develop a simple model to study classical fields on the background of a
fluctuating spacetime volume. It is applied to formulate the stochastic
Einstein equations with a perfect-fluid source. We investigate the particular
case of a stochastic Friedmann-Lema\^itre-Robertson-Walker cosmology, and show
that the resulting field equations can lead to solutions which avoid the
initial big bang singularity. By interpreting the fluctuations as the result of
the presence of a quantum spacetime, we conclude that classical singularities
can be avoided even within a stochastic model that include quantum effects in a
very simple manner.
