In what form was the space at singularity? It is somewhat imaginable for all the matter or energy to be condensed in sub-atomic size. But what about space? The space is neither 'matter' nor 'Energy'.  

If there were no space at singularity where did it come from?
A singularity in the strict sense is not assumed in the beginning of the big bang, but instead a Planck epoch governed by a yet to confirm quantum gravity. General relativity and quantum theory, are not consistent in this phase. This means, that space and time, if they existed at all in some sense, didn't follow the laws of physics we inferred from experiments.

This epoch is thought to have been followed by a grand unification epoch, where gravity is already separated from a unified strong, weak and electromagnetic interaction.

Then inflation is thought to have followed, "driven by a negative-pressure vacuum energy density". That's when spacetime expansion is thought to have accelerated rapidly, weak and electromagnetic interaction still unified.

All this is thought to have happened within the first $10^{-32}$ seconds.

Most of the physics in those early phases is not (yet) accessible to experiments. A few cosmic ray experiments may try to look into the energy ranges, thought to have been present in the early epochs of the universe.

More on the chronology of the universe.