For a massless particle the spacetime interval between its point of emission and point of absorption is zero: the two points coincide. From the vantage point of such a particle space-time has reduced to a single point.
In the Standard Model, all particles start with zero mass, so does this suggest that our familiar 4-D spacetime is a consequence of the Higgs field or some similar mechanism by which mass is acquired?
Note: if you believe the large-scale 4D structure of spacetime is a pre-existing given, this question makes little sense. In a relational view, where spacetime emerges out of event relationships, then the question suggests that a universe comprised solely of massless particles would have a fundamentally different event-structure.