"He is the Originator of the heavens and the earth. (The Qur'an, 6:101)"
1) You are begging the question - To take the Qur'an as truth you must first agree that God exists. So to use the Qur'an in your argument to prove God exists is circular reasoning.
"...the entire universe, together with the dimensions of matter and time, came into existence as a result of a great explosion that occurred in no time."
2) This may be splitting hairs, but it DID occur in a time - approximately 15 billion years ago by some current estimates. I think what you mean to say is that time did not exist before the big bang. But would there not have to be time before the big bang to say 'before the big bang' in the first place? To better understand what I mean, what would you say if I asked you "What is North of the North Pole?"
"... "The Big Bang" proved that the universe was created from nothingness as the result of the explosion of a single point."
3) Actually that is not really modern astrophysics anymore - the more plausible modern theories include quantum mechanics and the random fluctuations inherent at such small scales. They seem to imply that the universe [I]could[/I] have come from essentially nothing.
If you don't agree with #2, then consider this:
The universe is all that exists.
Before the universe, nothing existed.
Before the big bang, the universe did not exist.
Since God exists and the universe is all that exists, God is part of the universe (by this I mean that God is a subset of the universe).
Therefore, before the big bang, God did not exist.