You persist with this approach about science not being able to test the existence of gods. Hawking gave us a new angle on this if you would take note. With his in depth insight into his scientific speciality he observed there was no time for a creator to exist in.
"We have finally found something that doesn’t have a cause, because there was no time for a cause to exist in," Hawking wrote. "For me this means that there is no possibility of a creator, because there is no time for a creator to have existed in."
Can you make comment about this observation instead of beating that same old drum?
He didn't know that. He took the math within the field of physics, which is within the universe and claimed that could tell us if there is something or nothing outside the universe. That is not possible. What is on the inside of the universe can't know what is on the outside. You can only know that if you can check through observation. That is not possible.
Knowledge and science presumes time and space and takes place within the universe.
In other words the math he used for the calculation is inside the universe and the math can't cause there to neither something or nothing.
Notice this, from the OP:
"I think the universe was spontaneously created out of nothing, according to the laws of science," Hawking, who died in March, wrote. "If you accept, as I do, that the laws of nature are fixed, then it doesn't take long to ask: What role is there for God?"
That he thought something doesn't decide, if there is nothing or something outside the universe.
The same with the acceptance. That doesn't decide, if there is nothing or something outside the universe.
That was figure out by Immanuel Kant. You can account for human knowledge by listing, what human knowledge presumes.
That includes that we are in time and space inside the universe.
The only thing we can say about objective reality as independent of the mind, is that objective reality is independent of the mind.
And if you are not a solipsist, that the mind is caused by objective reality.
The rest is what axioms you use and what you can say about the limits of knowledge, reason and logic.
There is a reason, science is based on methodological naturalism.
https://rationalwiki.org/wiki/Methodological_naturalism
Methodological naturalism is the label for the required assumption of philosophical naturalism when working with the scientific method. Methodological naturalists limit their scientific research to the study of natural causes, because any attempts to define causal relationships with the supernatural are never fruitful, and result in the creation of scientific "dead ends" and God of the gaps-type hypotheses. To avoid these traps scientists assume that all causes are empirical and naturalistic; which means they can be measured, quantified and studied methodically.
The core axiom in science is that you start by assuming that the universe is natural.
But there is still a limit to knowledge and one of them is that we can't know what is outside the universe, nothing or something, because we can't check.
Hope it helps.