My take on this issue is one should keep in mind that GR is a 4-dim theory, i.e., one finds a stress-energy tensor (SET) and spacetime metric (g) that together satisfy Einstein's equations (EE) on the spacetime manifold. Let me explain.
Typically, one assumes a particular SET and then solves for g. In the standard GR cosmology models, the SET one starts with is a perfect fluid which allows the 4-dim spacetime manifold to be sliced into space-like hypersurfaces S of homogeneity and isotropy. The metric g is then split into a spatial part S and proper time T for observers at rest with respect to S. You have your GR cosmology when you solve EE for g on T x S.
Notice that your solution is a 4-dim manifold T x S with a metric g. Nothing is "happening." Nothing is "being created." All that dynamical talk, i.e., 3-dim entities evolving in time, happens when "the universe" is identified with S. At that point, one can tell dynamical stories where the 3-dim entity is the universe S. For example, one can ask what S was like at T = 1 billion years and how did it get to be like it is today, filling in all the details of temperature, energy density, etc, on S as a function of T. But, someone else could choose another 3-dim spatial surface and a tell different story. Granted their "universe" wouldn't be homogeneous and isotropic, but GR doesn't care, its solution stands unaltered. And, there are limits to what one can ask in this dynamical context. For example, one can ask what happened on S immediately before T = 2 seconds and tell a causal story about S(2s) based on S(2s - dT). But, once you get to S(0), there is no earlier S and your causal stories end. As Hawking said, "It's like asking what happens one mile north of the north pole, it's a meaningless question." You've milked the 4-dim GR solution for all the 3+1 dynamical/causal story it has to offer. As far as GR is concerned, the existence of S(0) is no more mysterious than any other event on T x S. You could equally ask, "Whence the event of me touching my nose now?" GR can't answer that either. All GR says is that whatever 4-dim spacetime manifold you choose, the SET and g have to be self-consistent, i.e., they have to satisfy EE. Dynamical stories are, in a very real sense, secondary and irrelevant in this 4-dim view.
“There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. In particular, one does not think of particles as moving through space-time, or as following along their world-lines. Rather, particles are just in space-time, once and for all, and the world-line represents, all at once, the complete life history of the particle.” R. Geroch, General Relativity from A to B (University of Chicago Press, Chicago, 1978) pp. 20-21.
