If we’re going to be careful with language, the word “prove” in the title should be replaced with the word “demonstrate.”
And while we’re at it, anyone interested in thinking should note that everything demonstrates God’s existence.
I did not ask the question, yet "demonstrate," or "evidence" still results in the same situation as being a position of faith, Biblically defined (confidence based upon evidential warrant) as it does for the deist. But my position is that To believe that an exceedingly vast, systematically ordered universe, exquisitely finely tuned for life with intricate astounding complexity, can be all a result of purely natural processes requires more faith, than that the universe logically testifies to design, requiring a First Cause (at the least), that of a powerful being of supreme intelligence being behind the existence of energy and organization of matter.
And while we’re at it, anyone interested in thinking should note that everything demonstrates God’s existence.
Yes, an ultimate uncaused cause, leaving the atheist to place some hope in the multiverse hypothesis being the possible answer. Of which even WP presently (subject to much change) states, "Although some scientists have analyzed data in search of evidence for other universes, no statistically significant evidence has been found. Critics argue that the multiverse concept lacks testability and falsifiability, which are essential for scientific inquiry, and that it raises unresolved metaphysical issues." (https://en.wikipedia.org/wiki/Multiverse)