"If somebody has initial precepts that says God doesn't exist, there's no way to 'prove' to that person that God does exist."
Incorrect, because while atheism may display the zeal of a religion, it is based on reason and a set of observable, objective principles that do not contain a presumption on God. If you show, in the framework of science, a divine action - something that violates natural law - and present convincing proof that this is the action of a sentient being whose capability transcends logic, then a scientist and an atheist will acknowledge the existence of God.
If you remember the recent discussion on the feasibility of superpowers, how I said flying like Superman or Nathan Petrelli is impossible because it violates conservation of energy - it is entirely possible to use logic to assess an unknown phenomenon. Even if the phenomenon's actual mechanism is not understood, it is possible to dismiss a hypothetical as possible or impossible.
Now, the reason why the framework of science is superior to the framework of faith is because the uncertainty of faith makes it self-defeating. If you strip away enough layers of abstraction, it comes down to practical use: if an act of God cannot be triggered reliably, if it cannot be used to achieve a particular effect, then the fact that occasionally its presumptions appear to be borne out by observation is irrelevant.
When you show me a toaster that works by the power of Allah, then we'll talk.