Actually, a more accurate description would that science is there to find out what happened and how.
Science is a method of inquiry. A very succesfull one, to get accurate answers to complex problems.
Indeed. Or even only supported, tested or falsified.
Exactly why science doesn't care about it. There is nothing "there" to investigate, study or test.
Why would science include parameters that can't be shown to be real or have any kind of impact on anything?
No. Rather, God if included adds nothing of any value.
E = mc² + god. Work it out and test it against reality and "god" then gains the value zero.
As far as testability, observation and experimentation goes, gods are indistinguishable from non-existance.
And the same goes for anything else your imagination can produce which is defined as undetectable without any kind of measureable manifestation.
Why is that a problem?