The Big Bang is a theoretical event when the expansion of the universe began from a single point, i.e., began assuming space dimensions. Observation shows the observable universe expanding, and if that expansion has "always" happened, projecting back sufficient time, there would be an instant when the universe expanded from a single point. Current observation places the moment at about 13.8 billion years ago, a precise time requiring determination of the Hubble constant and its variation over time (cosmological constant/dark energy).
Though the finite speed of EMR allows us to observe past times by looking long distances, our ability to observe detail in the era of such a theoretical Big Bang is limited, i.e., we can't say with much certainty what happened. However, the notion that expansion has persisted since that general time (the Big Bang theory) is well-established by observation and generally accepted, and no alternative scenario to a Big-Bang instant has any more evidence. Cosmology does explore scenarios all the way back to the apparent instant of the Big Bang, applying the known laws of physics.
Before the Big Bang was postulated, the tacit assumption was that the universe remains the same, and when the idea of expansion was introduced, the older assumption was termed a steady-state universe. It was this assumption that led Einstein to include the cosmological constant in general relativity's field equation, and for some time after the universe's apparent expansion become evident, serious theories of how the universe might be "steady state" continued to be developed.
The term standard Big Bang (SBB) refers to a "working model" version of the Big Bang theory specifically assuming that physics and physical constants at the time were the same as now. (Other theories might speculate that some constants have varied according to the size/spread of the universe.)