You are right, time is not a dimension but the order of events. But we can go even further and say that there are not even 3 "special" spatial dimensions.

For any material entity, the only thing that really exists at any moment are the interactions that shape it and inform it about everything else existing out there. These interactions, whether internal or external, are just instant connections between past and present events that satisfy the light-speed ratio at all times, so it doesn't matter how distant or past the events to which they connect, these interactions are instantaneously present to the entity they form, conforming its reality. They make up the 13.8 billion light-year universe that unfolds before our eyes. Each entity experiences its own universe of interactions, remarkably similar to the one that has gone before or to that of other entities nearby.

In this sense, the universe doesn't even have 3 spatial dimensions, but infinitely many. Any interaction fulfilling the light-speed ratio could be considered a dimension. It just so happens that we can express this vast number of unfolding relationships in an arbitrary 4D grid system we call spacetime.

Time would be the ordered sequence of interactions we experience (so we need one dimension for that), and 3D space would be the simplest static coordinate system we can derive to make sense of the incredibly outstanding number of light-speed connections that make up ourselves and the universe we experience.

But the fact that we can express everything real using just these 4 numbers doesn't make them any more real. They are useful abstractions based on the "distillation" of the real information that conforms us and reaches us, but nature doesn't know about them at all, only about the instantaneous interactions that unfold, which are experienced as energy or information exchanges at the speed of light by the very same patterns they help to create, which they picture as other patterns laid out in 3D space and evolving in 1D time.