Could God prove His existence through irrefutible logical arguments?

"He has through the impossibility of an infinite regression of cause and effect. There must be a first uncaused cause to initiate this cause and effect sequence resulting in the world as it is. This elementary but profound logical argument is simply ignored in favor of believing that something spontaneously arose from nothing. Even the lyricist Oskar Hammerstein knew that nothing comes from nothing and nothing ever could."