Q: Can G-d’s existence be proven beyond reasonable doubt?

A: No. Not rationally, logically or with human reasoning. Using the scientific method the existence of G-d cannot be proven. G-d can be experienced by the individual or a group, but can never be proven. Any god whose existence can be proven using human logic and science will not be G-d. Why? Because G-d's thoughts are not our thoughts and G-d's ways are not our ways. It would be like an ant trying to prove or explain to his fellow ants what a human being is. An ant cannot prove our existence any more than we can prove G-d's. An ant can experience us but never fully understand, explain or know us. We live on two different planes of existence (different frequencies or vibrations) even though we may appear to be sharing the same space.