The scientific method is at its core pragmatism: Whatever works is accepted as truth until it no longer works. The scientific method does not show us "truth". It shows us the best-possible guess what the truth is, working with nothing more than the limited and error-riddled information we finite beings have.
Do you know how the scientific method came to be? Evolution. Science combined occult experimentalism with mathematics and it survived where other methods (such as hermetic magic) had failed because it was capable of producing practical results.
Up until the Middle-Ages the evolutionary pressure was that a world-view must provide a stable society, and that's why religion ruled supreme since the ancient days. Then the zeitgeist and the evolutionary pressure changed and now a world-view was supposed to provide practical results. And that's why science replaced religion as the dominant world-view.
There are other methods. Flat-Earthers love the zetetic method. It's related to the scientific method but considered better because it's not "mainstream-science". But it has a barely visible yet massive math-error in its structure. Therefore the zetetic method's logic is simply invalid.
Goedel made a mathematical proof that a supreme "good" must exist, however his proof contained lots of unrealistic assumptions, such as the world being clearly divisible into good and evil.
As for belief... I don't trust belief. A logical conclusion derived via belief always depends on the subjective entity who made that proof.
EDIT: It is possible that there is a method out there that is structurally capable to allow for a finite being like us to prove/disprove an infinite being like God, but we don't know that method.
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