J. Richard Gott and one of his students at Princeton wrote a paper several years ago proposing the possibility that a time loop existed where each event is preceded and followed by the same event. Like an episode in the Twilight Zone where the main character would wake up to the previous morning, there may have been such a rut that the dimension of time was curled up into. Entropy may have existed before the time loop broke its symmetry and may have been the cause of an asymmetry developing in the loop, allowing an expansion of the time loop into a future of never-before-events to occur.

Time, like space, may have expanded into today.

To ask what all 4 dimensions are expanding into has a relativistic underlying. Something else must not be expanding relative to it and that something else must further have an Aristotelian characteristic of being a special reference frame, violating the Copernican principle.