I saw the excellent answer here: Did the Big Bang happen at a point? but I have a hard time imagining the initial state. If the distances between all points in the universe were zero at the Big Bang, how is it not a single point in space?
We don't actually know what happened right at time 0 -- our present theories give a singularity there, an undefined point like dividing by 0. So it's not accurate to say it's a point, it's just something undefined. There is hope that a quantum theory of gravity might allow us to describe the beginning of the universe better, for example by providing a maximum density or other condition. But for any time $\epsilon > 0$ we can find in classical models a finite density of the universe, and space at that time is fully 3 dimensional. (It should be noted that the particular choice of time coordinates is somewhat arbitrary -- time is relative after all -- but the usual choice in cosmology is known as cosmic time in which the average density of the universe is uniform.)