Mathematically,R^3 space not being fundamental makes sense to me but physically i dont see how someone would get the intuition to think in that direction,
One explanation relies on a theorem of Malament that the causal structure of spacetime determines the metric upto a conformal factor. And this factor can be determined from specifying a density. Sorkin uses this in causal set theory with the spacetime manifold being emergent as a continuum approximation where order and number give geometry.