You’re probably referring to a state where all parts of the complete representation exist at the same time. Because if they don’t have to exist at the same time, then it might be possible to “write it down” if the universe has unbounded duration (“might” because I don’t know how the heat death plays into that). However, “at the same” time isn’t well-defined in relativistic spacetime. The sibling comments are definitely right with respect to the reference frame implied by the CMB. But I’m wondering if it wouldn’t be possible to slice spacetime in a way that actually makes a representation possible “at the same time” in some reference frame?