The interpretation usually given for Gauss' Theorema Egregium is that a being living on a surface with intrinsic curvature can detect that curvature just by walking around the surface and measuring angles and distances. With the advent of general relativity many years later, it became evident that the our 3+1 dimensional universe need not be flat, and the Theorema Egregium is the basis for several experimental efforts to measure the curvature of the universe.
Question: Did it ever occur to Gauss or other geometers of that era to measure the curvature of the universe?
[Bonus: If not, who was the first to propose that the universe might be curved? Einstein?]
I imagine there may have been a conceptual difficulty due to the fact that most differential geometry done in the early days was restricted to curves and surfaces, rather than 3-manifolds. But even in lieu of the proper mathematical machinery, I imagine someone may have realized that an analogous sort of curvature to the Gauss curvature of surfaces should be available for 3D spaces. Did anyone propose to measure such properties of space?