The answer is that we don't know. Why? Because the theory of gravity which we have and use, GR, has a singularity. Things which should be finite in a physical theory, like the density, become infinite. And theories with a singularity are simply wrong, they need a modification, and this modification is necessary not only at the singularity itself, but already in some environment of this singularity.
Moreover, we already know for independent reasons that a modification is necessary: Because if one looks at times $10^{-44}$ s after the singularity, quantum gravity becomes important, which is an unknown theory.
And we have also empirical evidence that the most trivial model based on well-established theories (GR with SM for matter) fails: It is the so-called horizon problem. It requires, for its solution, some accelerated expansion in the very early universe. 651
One can propose models which lead to such an expansion based on particle theory, theories usually named "inflation" (imho very misleading, as I explain here), but they usually use speculative extensions of the SM like GUTs, supersymmetry, strings and so on. So, even the details of a particle theory which would give inflation are unknown.
So, while big bang theory is well established, if one thinks about everything haing been as dense as inside the Sun, and I would say reliable if as dense as inside a neutron star, we have not much reason to believe that the theories remain applicable for much higher densities, and certainly not for the density becoming infinite.
From a purely mathematical point of view one cannot tell anything about the singularity itself too. If one considers, for example, the metric in the most usual FLRW coordinates $ds^2=d\tau^2-a^2(\tau)(dx^2+dy^2+dz^2)$, then the singularity would a whole $\mathbb{R}^3$. The limit of the distance between the points would be zero (which is the reason why one usually prefers the picture with a point singularity). On the other hand, the limit of what one point which moves toward the singularity can causally influence in its future remains (without inflation) a small region, which in no way tends to cover the whole universe, which corresponds much better with a whole $\mathbb{R}^3$ space singularity. 764