We don't know what shape the universe is. We only know that the
observable universe (what we can see) is a sphere, since it is based in the light that reaches us from all directions.
Space was everywhere immediately because space is what makes our universe what it is. This is a difficult concept perhaps, but no matter what shape our universe is it is possible to imagine a place where space (as we know it) does not exist. This would be "outside" our universe.
Matter is, ehm, another matter entirely.

Matter was not everywhere but *almost* everywhere. There are several theories on this but for sake of simplicity let's say that almost immediately after the big bang, matter formed. But it was not everywhere, and as the universe grew it did not get more matter so matter was thinly spread out whereas there was more and more space.
Hope that made any sense.