The entire theory of the big bang is contingent on the fact that gravity exists -- i.e. General Relativity describes the motion of the universe as a whole. It is not at all important what is inside the universe -- whether it be atoms, people, electrons, or purple unicorns. We expect General Relativity to be correct up until very early after the big bang, something like 10^-40s to be conservative (roughly the Planck time).
Before this time, we expect some manifestation of what we call gravity to be present, but likely one needs to account for quantum corrections.