Describing space(-time) is really tricky.

Dimensions are to space-time as colour is to paint, but just as the colour is not the paint, the dimensions are not the space-time. Space-time can have any number of dimensions, just as paint can be any colour, and while the dimensions of a space-time are an important quality of that space-time, just like the colour of the paint, they aren't what makes the space-time in the first place, just as the colour does not make the paint.

So just as we might say we have a particular shade of red, or green or blue paint, we can have one, two, three etc. dimensional space (or indeed, space-time).

Time defines the position in a journey where space is moving or expanding.

In four-dimensional space-time you need four coordinates to define the location of anything, regardless of whether it is moving or not, for even if it is not moving through space it will still be moving through time.

Now although we can say that the universe started ~4 billion years ago, giving us a fixed temporal reference point from which we could in theory make our measurements, the rate at which things travel through time varies according to the speed at which they're moving, so if it were possible for a traveller to have set off on a journey when the BB occurred, at half the speed of light, and to then land on Earth right now, they wouldn't be ~4 billion years old, even though from our point of view they started ~4 billion years ago.

In spatial terms it's even more tricky because we don't have the spatial equivalent of the start of time that we have with the temporal dimension and this is largely because geometrical points cannot expand, at least in the sense that we're familiar with things expanding.

The problem here is that a geometrical point has zero size and no matter how you try to multiply it, it'll always have zero size. Now if the BB did indeed start from a geometrical point then the term 'expansion' is simply inadequate to describe what happened; rather than something very small getting bigger, something that appears to have had no dimensions or size, or had a dimensional order of zero, was raised to a higher dimensional order, and in fact, as far as we can tell, to four dimensions, which gave it a non-zero size and which allowed it to start expanding.

The cleverest bit of all though, is that the original geometrical point, having no size, was by definition uniform i.e. it was the same everywhere, so when it was raised to a higher dimensional order there could have been nothing to cause any non-uniformity between any two points in the resulting four-dimensional universe. The consequence of this would be that every point in the universe must be considered to be the same as any other point in the universe.

On the other hand though, if the singularity from which the BB originated had non-zero size, then it must have had at least one dimension, which implies that at least one dimension had to exist before the singularity could exist within it. A non-zero sized singularity too, already having a non-zero size, can quite happily expand, for simple expansion doesn't require an increase in its dimensional order.