The Big Bang theory refers to the origin of the entire universe, not just the observable universe. According to this theory, the universe began as an extremely hot and dense state around 13.8 billion years ago. It is important to note that the concept of the observable universe is different from the entire universe.
The observable universe refers to the portion of the universe that we can currently observe, given the limitations of the speed of light and the age of the universe. It is the region from which light has had enough time to reach us since the Big Bang. The observable universe is estimated to have a radius of about 46 billion light-years, which is larger than the universe's age because the fabric of space itself has been expanding since the Big Bang.
Regarding your statement about the Big Bang being a quark exploding, it is not an accurate representation of the theory. The Big Bang theory describes the initial expansion and subsequent development of the universe as a whole, not as a single quark exploding. It is a complex event involving the rapid expansion of space and the subsequent formation of particles, atoms, stars, galaxies, and clusters of galaxies over billions of years.