You can demonstrate evolution - but you can call on it to be demonstrated. For instance you cannot make a monkey turn into a man. Humanity has no control over evolution - evolution it greater than man. If man could change evolution - then evolution would not exist in its current state. Yet, you ask Christians to call on God and for God to give you a demonstration. God is greater than humanity, if humanity could make God do something - then humanity would be equal to God and God would not be God. Therefore we can only use past demonstrations of God as perceived by human experience. Those things passed orally and through writing have come to be known as the Bible.
And what's in the Bible can be tested against what we know of reality, to see if it's true.
As it turns out, the parts we can test about what "God" has done, aren't true. The book of Genesis is the prime example of this.
To keep with your analogy, the Bible is like a faked scientific experiment that has since been falsified.