This is a very good question to get at the heart of a very misunderstood concept. The modifier of "scientific" on the word evidence limits the concept drastically. Evidence as used in science is that which relates to a scientific theory or proof of some kind. God, philosophy, law and medicine have different kinds of evidence for their own school of thought.
So what is evidence in a court of law is not necessarily evidence to a GP trying different ways to cure an ailment. General Practice being more a combination of art and science, and law having to do more with nebulous concept of what is more likely than not or beyond human understanding to be different.
So you do not snatch the scientific evidence of gravity to prove a philosophic truth of our existence being "proven" by the fact we think. (Cogito Ergo Sum)
I tracked in wilderness for some time. Evidence of the fact that several deer passed through in a certain direction at a run about 2 hours ago is neither scientific or legal evidence.
So no, you do not mix and match different evidence from one area of study and understanding to another. That is unless the discipline combines two as a principal -- General Practice of Medicine. Sociology and other behavioral "sciences" to this day are considered not science by many in science.
I could easy claim that the mere fact of our existence is proof of God. And it is in theology but that does not apply to scientific inquiry.