Occam's Ghost, you are both right and wrong.

You are correct in that in terms of relativity, space and time are treated mathematically as an entity together. Despite this however, the way that space and time are treated is slightly different from one another. Check the literature.

The observed expansion of the universe is explained by General Relativity as an expansion of the metric with respect to time. A metric is simply a way of defining a coordinate system so that you can measure distances between two points.

So, your initial assumption that spacetime is expanding is borne out of a misunderstanding of relativity. It is like asking everyone here to prove that apples are oranges. With respect, it is a nonsensical proposition.

Hope this helps.