It does not deal with a singularity. The Big Bang model deals with the development and evolution of spacetime from a certain point in time forward to the present but it does not deal with the physical creation of the Universe.
--We cannot test whether or not the universe came from something; If you imagine a bubble being pushed from one plane into another, there would appear to be nothing, then a point, then a surface, then a bubble expanding outwards. No singularity is needed to explain this.
--We cannot test what existence there was prior to the Big Bang.
--We cannot test what caused the Big Bang
It is for these reasons that the Big Bang does not deal with the Birth of the Cosmos. It appears to infer it, but that is all it does. Because we simply do not know.
And in science, it is ok to admit that you don't know something without feeling the need to just make something up or speculate wildly to fill that gap.