The short and rough answer to your question is, space and time banged out of the big bang.
Exactly how, is a mystery.
If I knew the answer to that, I would be guaranteed the next Nobel in Physics.
But I know what line of investigation one needs to follow to get the answer to the how of your question.
To understand that, one needs to reconcile Einstein's theory of Relativity with Quantum Physics.
If at all you subscribe to the Big Bang Theory as an explanation of the beginning of our universe - it is the most widely accepted theory- and follow the explanation, the Big Bang came about some 13.7 billion years ago. It comprised of an intense explosion - for lack of a better word, mathematical equations fail in a singularity, let alone words- that came from an infinitesimally small point. This point, essentially, contained all the mass and space we have in the universe today.
Eventually the point exploded to the size of the universe today. The details are lengthy and, some are beyond what I could articulate. Authors such as Stephen Hawking in "A Brief History of Time: From The Big Bang To Black Holes" and Stephen Weinberg in "The First Three Minutes: A Modern View of the Origin of the Universe", both exellent books on the subject I have had the pleasure of reading, explain the issue better than I can.
The difficulty in determining the answer to your question, what really banged from the big bang, lies in the fact that our current mathematics is not equipped to answer that. We have the mathematics to deal with the very large, very massive, very far away (think stars, galaxies etc). That is Einsteins Relativity. We have a sufficient understanding of the mathematics to deal with the very small, infinitesimally so, very light things like subatomic particles such as electrons, neutrons, even quarks and neutrinos etc. That is Qquantum Physics.
The trouble with the Big Bang, per the theory and mathematical model, it is that, it requires something that deals with both the very heavy and dense and infinitesimally small at the same time. This is because the "explosion" happenned at a point that was both infinitesimally small and that had extremely unimaginable density. Imagine compressing all the mass of the universe in a point that has practically zero space.
So, our mathematics is not able to solve the necessary equations. We need to get a new math. If we use Relativity, it can deal with the mass of the big bang, but it cannot deal with the space. If we use Qquantum Physics, it can deal with the space of the Big Bang, but it cannot deal with the mass. It is almost like you have a camera, but because of the way the lens works, if you have two people, one near you and another far away, you cannot focus to get both people to look clear in the picture.If you get the person near you looking clearly, the person far away will look out of focus, if you get the person far away looking clear, the person near you will look out of focus. You need a new camera.
When theoretical physicists try to solve the equations using existing math, they get what is called "singularities". A singularity is a point where mathematical equations break down and produce nonsensical answers. A few days ago, my friend
Zurri tried to prove to me that 1=2. But his equations were flawed, because he had a singularity. His singularity was "division by zero". Division by zero is forbidden in most of Mathematics, because it produces a singularity that eseentially will eventually mean any number is equal to any number.
This is why Zurri was able to prove 1=2 by using that singularity. With a singularity, anything is possible.
Usually mathematicians/ physicists cancel singularities with other singularities. But in the math of the Big Bang, they have not been able to do so
So we need a new math. The experts call this reconciling Einstein's Relativity with Quantum Physics. Quantum Gravity. String Theory also attempts to solve this. But some of the solutions of String Theory require excessive energies, such as a particle accelerator that is as big as the Solar System (theories are tested by accelerating particles to high speeds and observing their behavior, one such particle accelerator is the Large Hadron Collider near Geneva Switzerland)
I have tried to explain and answer this difficult question as much as I could with the limited lay reading I have done as my guide. I am attaching the two books I mentioned above for further reading.
The short answer to your question is space and time banged.
The how of this, is still a mystery.