How did the Big Bang create the universe?
The 'Big Bang' is what we call the furthest back in time we can trace the Universe's history. We have a solid understanding of what happened fractions of a second after 'time zero', but cannot yet say anything about before.
Saying 'the Big Bang created the Universe' is a misnomer. It's more accurate to say 'the Big Bang was the beginning of our Universe (and is as far back as we can study it)'.
The 'Big Bang' both broadly describes a period of exponential expansion at the beginning of our universe (remember, it's still expanding!) and a specific event at what would be 'time zero'.
Our theories break down close enough to 'time zero' ( we cannot model the universe between t=0 and about t=0.0000000000000000000000000000000000000001 seconds. Seems like a negligible time period, but important things must have happened during this fraction of a second!).
Nevertheless, after this time, the universe continued to cool exponentially, and eventually quarks became nucleons (protons and neutrons) and eventually into atoms. After light stopped interacting with matter, those atoms were free to gravitationally collapse first into stars, and later into galaxies and planetary systems.