Therefore, unless man can provide a provable explanation, using empirical evidence, of where, when and how space, matter, energy and time came into existence and in what sequence, I choose to believe in the supernatural.
The empirical evidence for the 'Big Bang' (the expansion of the universe from an initial state of high temperature and high density) is the observed redshifts of the galaxies, the presence of an almost isotropic cosmic microwave background, and the isotopic and elemental abundance ratios D/H, He-3/H, He-4/H, and Li-7/H. The cosmic microwave background is interpreted as the redshifted radiation of the fireball of the 'Big Bang'.
The age of the universe follows from the relation between the distances and the redshifts of galaxies and quasars, and it is confirmed by the ages of the oldest stars derived from the H-R diagrams of globular clusters. The most recent measurements give an age of 13.8 billion years for the universe, and this answers the question when 'space, matter, energy and time came into existence'. So far as I know, these quantities came into existence everywhere, throughout the universe, although at the beginning the universe was much smaller than the nucleus of an atom. As to how they came into existence, I don't know.
As to the sequence, according to chapter 6 of
The Grand Design by Stephen Hawking and Leonard Mlodinow, 'In the early universe - when the universe was small enough to be governed by both general relativity and quantum theory - there were effectively four dimensions of space and none of time.' This implies that space came before time. Also, it appears that energy came before matter; the first 'elementary particles' of matter (quarks and gluons) came into existence about a trillionth of a second after the origin of the universe, when the temperature was about 1 trillion kelvin. - see
Chronology of the universe - Wikipedia .
You asked a question, and I have tried to answer it. If you want any more information, and if you want to find out more about the empirical evidence that supports these conclusions, you will have to read books, scientific papers and websites about cosmology. However, I would emphasise that the 'Big Bang' cosmology is supported by abundant empirical and theoretical evidence, from both astronomy and fundamental physics, more evidence than can be contained in the space of an internet forum.