How did the Big Bang begin?
It was the beginning of the evolutionary epoch in the history of the Universe.
At Planck time (which is the earliest possible instance when time can be measured) symmetries were broken and the Universe entered the evolutionary phase (which was inflationary). Space-time became a tangible entity which we identified as the Universe. This is distinct from a singularity, which is what the primordial Universe was, before the Big Bang.