According to this theory, the universe began, as aforementioned, with the burning of a colossal band of gases and dust. These dust and gases accumulated over time and eventually started clumping together, and the friction from this clumping eventually caused burning.
All of this burning is what began many clusters of stars. Over time, these clusters went supernova, and caused a lot of debris and gas and materials to scatter and coalesce into various celestial bodies.
How do we know that these are facts? We don't. They're just widely supported and accepted scientific theories, developed over time by philosophers and scientists alike. Scientists have used tools to measure EM wavelengths, view the rest of the universe, and even explore other planets, and these tools give us clues to what the 'big scheme' is.
There are multiple different beliefs about the big bang in different cultures, though. For example, creationism is the belief that the universe was created not by a big bang, but was from a divine being's creations.