It is possible that both the classical description of spacetime and the rules of quantum field theory emerge from a more-fundamental structure of physical law. Pregeometric frameworks transfer some of the puzzles of quantum gravity to a semiclassical arena where those puzzles pose less of a challenge. However, in order to provide a satisfactory description of quantum gravity, a semiclassical description must emerge and contain in its description a macroscopic spacetime geometry, dynamical matter, and a gravitational interaction consistent with general relativity at long distances. In this essay, we argue that a framework that includes a stochastic origin for quantum field theory can provide both the emergence of classical spacetime and a quantized gravitational interaction.