Ortho:
Natural science is the stury of natural phenomena using the scientific method. Natural science is confined to the natural realm. God is not detectable by natural science since God is not in the natural realm.
The teaching of the Church, notwithstanding what your scientists might say, is that God is knowable by the light of natural reason apart from religious revelation. Since only the natural realm is within the grasp of natural reason, this means that God is knowable by looking at the natural realm. The natural realm is also knowable as a work of God.
Catechism
scborromeo.org/ccc/para/50.htm
50* By natural reason man can know God with certainty, on the basis of his works.** But there is another order of knowledge, which man cannot possibly arrive at by his own powers: the order of divine Revelation. Through an utterly free decision, God has revealed himself and given himself to man. This he does by revealing the mystery, his plan of loving goodness, formed from all eternity in Christ, for the benefit of all men. God has fully revealed this plan by sending us his beloved Son, our Lord Jesus Christ, and the Holy Spirit.
scborromeo.org/ccc/para/39.htm
39
In defending the ability of human reason to know God, the Church is expressing her confidence in the possibility of speaking about him to all men and with all men, and therefore of dialogue with other religions, with philosophy and science, as well as with unbelievers and atheists.
scborromeo.org/ccc/para/37.htm
37 In the historical conditions in which he finds himself, however, man experiences many difficulties in coming to know God by the light of reason alone:
Though human reason is, strictly speaking, truly capable by its own natural power and light of attaining to a true and certain knowledge of the one personal God, who watches over and controls the world by his providence, and of the natural law written in our hearts by the Creator; yet there are many obstacles which prevent reason from the effective and fruitful use of this inborn faculty. For the truths that concern the relations between God and man wholly transcend the visible order of things, and, if they are translated into human action and influence it, they call for self-surrender and abnegation. The human mind, in its turn, is hampered in the attaining of such truths, not only by the impact of the senses and the imagination, but also by disordered appetites which are the consequences of original sin. So it happens that men in such matters easily persuade themselves that what they would not like to be true is false or at least doubtful.*
What experiment can one do to detect God?
That God cannot be subject to an experiment does not show that God cannot be known by the light of natural reason; it only shows that there is something seriously wrong with your conception of what constitutes natural science. Keep in mind that at one point what we now generally call natural science was, more or less, what was called “natural philosophy” years ago. In fact, I believe that in England it is still called that at least in the honorary titles accorded certain scholars who occupy certain esteemed positions (chairs).
Natural science simply does not include God.
An assertion does not make a fact except for the fact that you made one. That God exists is a fact, a fact knowable by natural reason as well as one knowable by the light of faith, whether you recognize it to be one or not.