Re: “Ultimately, science is the product of experience, and that does not require even a knowledge of god. How do you explain tool-making by certain animals?”
I agree that knowledge of God is not required for the scientific method of experimentation to work - knowledge is knowledge whether the scientist believes in God or not - the laws of physics work whether or not one is a theist or an atheist. Gravity causes a theist or an atheist to fall. Brain size and intelligence that allows certain animals to “learn” from experience does not exclude God as being a creator of them.
If God created the universe and the laws of physics, all of it works as designed whether a human believes in His existence or not.
If god did not create the universe and the laws of physics, all of it works whether a human believes or not.