When I have asked Atheist's, a question like "What science do you feel Supports the non existence of God" Predictably The Atheist has responded with "There is no Evidence or Proof of God & Science requires empirical Evidence."
Your statement above is correct. In your post you also explain why this reasoning is supposedly incorrect. However by your own measure -
One also cannot prove that Elves do not exist.
One also cannot prove that Fairies do not exist.
One also cannot prove that Lord Xenu does not exist.
One also cannot prove that the universe is not the ejaculate of a Giant Space Penis.
So based upon your reasoning science cannot make any statements about the above because it can't disprove these examples empirically.
Absence of evidence is good enough to discount ALL of the above for any practical and scientific purpose. For example: When botanists study pollination of plants, they do not seriously consider the possibility that fairy's do this job at night. They don't present this as a possible alternate theory in scientific papers. Why? It is inefficient because it clouds the real evidence (insects, wind etc) for pollination and does not contribute anything to an understanding of the subject. Now if solid scientific evidence were to emerge for fairies pollinating plants then it would be incorporated into human scientific knowledge and would alter humanities perspective accordingly....
The simple facts are as follows:
1. Ordinary claims require ordinary evidence.
2. Extraordinary claims require extraordinary evidence.
Science is Atheistic, Aelveistic, Afairyistic, Axenuistic, Agiantspacepenistic. However it always remains open to the possibilities if serious scientific evidence were to emerge.