The cosmological model is a mathematical model built on General Relativity. The metric of general relativity is four dimensional.
The observation of "everything moving away from everything else" cannot be fitted in three dimensional space logically. It looks as if there is an explosion everywhere, in every (x,y,z). Why need an explosion? To explain how the energy came to be. So it cannot be fitted in three dimensional space gravity with a reasonable model.
A calculable two dimensional mathematical model, of everything moving away from everything else can be found in the balloon analogy. As a balloon expands, everypoint on its surface moves away from all other points. Unfortunately, we observe the galaxy expansion in three dimensional space and we need a fourth dimension to have the mathematical analogue. Which brings in the model of General relativity, which carries the concept of space expansion as the simplest mathematical formulation to explain why everything moves away from everything else. Mind you, GR fits all observations and experimental data up to now.