I think Joz is giving you the right answers, but maybe it would help if someone else took a shot at this.
Science takes no position one way or the other on things for which there is no evidence. Since there is no objective evidence for God one way or the other, science neither admits nor denies God's existence. It takes no position one way or the other.
You are naturally correct when you say there are more things in heaven and earth than are dreampt of in the philosophy of science, but science is merely a method for finding out all we can about the natural universe. The spiritual universe requires a different approach.
--Percy