Whatever you use to describe the geometry of the spacetime, I really find difficulties to comprehend they can contain all the infomation of the past of the universe.There is no such thing. The geometry of spacetime does not change. Spacetime is a 4-dimensional geometry that already includes all the information about what we normally think of as "change" over the entire history of the universe. What we call "change" is not the geometry of spacetime changing; it is just looking at different segments of our worldlines that lie in different parts of the unchanging spacetime geometry.
Also, as I have already said, there is no way to identify "corresponding points" in different geometries, so the conceptual picture you are implicitly using when you think of "geometry changing" is not well-defined.