According to the Big Bang theory, our universe started out as a singularity. In what did the singularity exist if nothing existed prior to the Big Bang?
No one knows for sure.
This is a question that still lies outside of our knowledge, and may always continue to do so. Physics today can do a creditable job of outline the events that took place following the explosion of that singularity (starting at about
A singularity occurs when the equations, in this case of General Relativity (GR), have a condition where a division by zero occurs. In terms of GR there are singularities at the Big Bang and in black holes. When a singularity occurs in equations of physics it means that the equations break down and can't describe the event as they stand.
General Relativity describes the universe well except in extreme conditions such as the Big Bang. Quantum effects would dominate at such conditions and currently General Relativity and Quantum Mechanics have not been unified. We need new theories to describe the Big Bang.
Also, it makes no sense to say "before" the Big Bang. All time and space was created at the Big Bang, so there was no before.