I understand that in general relativity all observers agree on what it is they see (looking at the same object or event) when they account for the effects on their observations of the gravitational field they sit in, on their distance and motion relative to the observed.
Does this mean that in general relativity there is a universe-wide present all objects and observers everywhere live in (so they are contemporaries, living at the same moment in cosmic time, X years after the big bang), but that it only for practical reasons—for example, time dilation and the (finite) speed of light which makes that we see a distant galaxy as it was in a distant past—that it cannot actually be observed?