Actually this is the exact same vision/intuition I got on a journey too. Alan Watts talks about this I believe in 'The book on the taboo against knowing who you are'. Fundamentally you are correct: a discrete 1D set can be represented as a perhaps infinite number of 0D elements; a discrete 2D set as a number of 1D sets of 0D elements, etc. This is standard practice in programming. Keep in mind you are looking at it through the lenses of a being that experiences linear sequences, linear time. There isn't really any need to have it go from 0D and iterate until it reaches 4D, it can explode into 4D straight away.
Another way to look at it is that emptiness/nothing is this infinite expanse like glass. As it is totally empty, like an infinite block of glass there is no way to tell anything is there so it appears as empty.
Then you introduce an event which begins time and creates the dimensions innately; this event is basically a fluctuation. The fluctuation 'shatters' the glass and as such the entire universe materialises 'everywhere' at once just as when a car window shatters, the entire thing becomes opaque. This is called 'the big freeze' and is proposed by some researchers at present under a new theory called 'quantum graphity' (
click for more details).
Here's my interpolation on this - at this moment however this is still a singularity of sorts as there is no meaningful element of 'size' because the energy density is simply too high and the information content of the universe at this present time is like 1 bit large. Then you get a self interaction which creates an infinite number of observable universes interacting with each other (i.e. all observable universes encompass the entire 1 bit omniverse) and the corresponding anti-collapse pressure of the information/gravity/mass-energy drives time forward causing entropy to increase and observable universes to expand. This process could have happened an infinite number of times with the universe created and immediately collapsing or lasting briefly before collapse but we would never know.
Regardless, the self-interaction of these observable universes observing each other and creating stuff from the quantum foam drives the universe to rapidly expand and that would be 'inflation'. Over time, complexity and constructal flow creates a means of encoding information such that inflation is no longer necessary to prevent gravitational collapse. At this point the omniverse has reached a level of complexity such that the first data compression algorithm exists and of course it immediately utilises this. The perpetual increase of information content drives the universe's expansion continually forward however as otherwise it would collapse and start over.
Just a bit of speculation, hehe.
