Special relativity gives us many "now slices." But the "now slices" for different observers moving at different velocities cut the 4-D universe at different angles--that was the clue that led to the understanding of a 4-dimensional continuum.
That's why Brian Greene, in his book "The Fabric Of The Cosmos" spent so much time developing the loaf of bread analogy with the slices of bread sliced at different angles. He associated physical reality (the entire 4-dimensional universe) with the whole loaf of bread and associated the different slices with the different 3-D universes that different observers live in at any given instant of time (different "now slices").
And that's why so many physicists have been captivated by the concept of the block universe. Paulselhi, I think you would be interested to google "block universe."