When Father Lemaitre (a priest who happened to be a good astronomer and a very good mathematician) tried to explain the apparent expansion of distant galaxies (which he had measured with the astronomer Edwin Hubble), he used the analogy of an explosion. (The Primeval Atom Hypothesis, 1927).
By the time he developed the mathematical model to explain the expansion of space itself, the explosion had been removed. It is space that expands, thus ever increasing distances between galaxies (as long as they are far enough apart to not be gravitationally bound). This was in the early 1930s. Father Lemaitre and Albert Einstein toured together to explain this model to other mathematicians, because it is difficult to understand the mathematics behind it.
Using the mathematical model and better observations of galaxies, a theory was finally developed, and published in 1948. The major difference between a hypothesis and a theory is that the theory makes predictions about what you should be able to measure if you were given better instruments, and - just as important - what you should measure if the theory was wrong. The theory must be "falsifiable" (the author of the theory must provide ways to prove it is wrong).
In the theory (published 1948), there is no explosion.
A famous astrophysicist hated the theory because it came from a priest and some people were using it as evidence that the universe was "created" (the astrophysicist was an atheist - he publicly said so himself). He created his own theory (1949) and, during a radio interview, came up with the awful nickname "Big Bang" for the other theory (because everybody had heard about the 1927 description with an explosion but not everyone understood the 1930 mathematical model that removed the explosion).
The name stuck.
And for 15 years, most scientists preferred the 1949 theory to the Big Bang theory, mostly because the mathematics were A LOT simpler to understand and, until they got better radio-telescopes, in 1964, it was just as good at explaining what we saw.
The name Big Bang is unfortunate because many people think that it describes an explosion. It does not.
Many people (including Father Lemaitre himself) thought that the Big Bang theory describes the creation (or start) of the universe. It does not. It simply describes the evolution of the universe's energy content over the last 13.8 billion years.
The "domain" of the theory begins at a moment called the Planck Time (13.8 billion years ago) when the energy density of the universe gets low enough for us to understand how things work.
At the Planck Time:
-- the initial energy already existed.
-- space was already expanding.
-- the energy density was NOT infinite (no singularity)
-- matter did not yet exist (the theory does explain how matter forms from the initial energy).
Therefore, something existed "before", but the Big Bang theory cannot tell us what, since its domain cannot go "before" (in fact, we don't really understand what the word "before" means when applied to the Planck Time).
There are many ideas, of which roughly eight or nine have some serious scientific foundation.
It could be that the "driving force" (or a triggering event) is one of those eight or nine... or it could be something else.