You make good points... unfortunately there can be scientific proof if you make up your own definition of "SCIENTIFIC".
This is exactly why I use basic, foundational science to show that God exists.
Everyone understands basic entropy a little. We all can see it in old age. Scientific laws regarding it are readily accessible in books and the internet. Scientific theory that tries to explain how it works, still doesn't understand it. But entropy is observable all around us.
Certainly science understands complexity more than anyone. Medical science has been trying to cure all kinds of diseases for ages. Nature is so extremely complex, that science has been failing with many of its cures. If science has been able to extend the length of lives of people, it isn't by much. Consider billionaire David Rockefeller. He died at age 101. If science had been able to keep anyone alive and young, he would have paid for it with his $billions.
Cause and effect is the basics of science. Scientists continually try to find the scientific causes that make/made everything that exists. Whatever they research, they continually look for the cause of it. No spontaneous generation of anything has ever been found. There is always a cause for something.
These 3 - cause and effect, complexity, entropy - point to the existence of God. How does it work? Like this.
Entropy shows that there was a beginning. If there had been no beginning, and if everything had been going on as it is forever, entropy would have destroyed all complexity long ago. Because the complexity is as great as it is, there was a beginning, and not too far in the past.
Entropy also shows that complexity is running down. In general, the past was more complex than what exists today. We do not find complexity coming out of something less complex, except temporarily. Now and again a couple of low intelligence will be parents of a genius. But the genius genes were inside the parents, even though they were not evident in the parents themselves. Complexity is always waning because of entropy.
Cause and effect is the greatest. Everything has a cause... or many causes. And the causes are effects of other causes. Like entropy and complexity, cause and effect are all-pervading... present throughout the whole system of nature.
In the same way that you can cause something complex to happen - if you think about it and plan it out and do it through cause and effect - even so nature has a complex plan built into it. How often do you throw a handful of sand into the air, and reap something complex that you can understand? The way the sand lands may produce a complex pattern, but the complexity of even that is beyond understand. It takes great working among people to produce complexity that is slightly great - automobile, computer, rocket, good medicine, etc.
The point? Whatever set cause and effect into place, to produce the complexity of life through essentially throwing a handful of sand into the air, must be extremely complex within itself. And since the complexity in us includes intelligence, emotion, thinking, feeling, and a host of other complex things, such complexity must be withing the "genetics" of whatever started cause and effect.
The best understanding of what this starter of cause and effect is, is found in our word "God."