We have a classical model of the universe without having ever observed it as a whole. There's also some philosophical debate, whether cosmology is really science since it assumes the Copernican principle without being ever able to test this hypothesis by observation or at least only to a certain extent.
That's why it is so complicated to get a clue about the quantum theory of gravitation: To get an idea, how to describe it, I think we'd need some phenomena related to it, and such phenomena are available to us only in a quite small piece of the universe, i.e., sufficiently close to us. Maybe we need strong gravitational fields to see deviations from classical behavior like better and better observations of black holes in our and other galaxies. Who knows?