Dear Roger
if I understand your position, you want to figure out how can make sense the notion of "space" in the presence of just few events. The answer is: it will make no sense. Think about: what is space for you? You can move in space, you can rotate something, you can walk, look at a distance ... the whole scenario makes sense only in the presence of infinitely many events, or, what we simply call "objects" that are macroscopical and made of a huge number of tiny parts, atoms, molecules, ... Whatever is "extension" needs parts, and not just a few of them.
Therefore, to figure out what does it mean to live with few "entities" and without space, try to imagine that you are an amoeba or any single-cell organism, that has no sight, no hearing, no other sense but e.g. three different kinds of different inputs--call them "a", "b", "c"--that are binary (on/off). Suppose also that the amoeba has brain that is a small subroutine, which is able to discover relations and causal connections. Such a mini-brain would figure out a space which would look similar to a finite group.
For a space like ours, we need to figure out infinitely many potential relations, corresponding to an infinite group. Such a group will be, however, finitely generated, by few simple relations, a bunch of translations, whose number of independent ones will define the space dimension.
Have fun
Mauro