Heisenberg was not trying to prove the existence of God as his statement itself says the essence of the universe is beyond the conceptualizing mind and proof is something within the conceptualize mind. It is a concept of the mind. That's not to say we can't learn more and more about the universe but he seems to suggest we will never get to the essence itself. That appears to be what his statement means. And my understanding of what he is trying to say is the following:I did take quite a lot of physics with my mathematics degree. It's worth the effort.
Still saw no evidence for god though.
Everything we have discovered so far has turned out to be "not magic".
Before we can have any concepts for or understanding of anything, we need a comparative or relative context. But since existence or life (whatever word you want to choose) is the ultimate context that allows for contexts themselves, then one would have to put the ultimate context within itself, which would appear to be logically or even conceptually impossible or at least logically faulty. To FULLY understand anything, one would have to be inside of what we are trying to understand, but also observe it from outside of it as well, because part of having a complete understanding of something requires that one see or observe it in a detached view outside of the thing itself. So our understanding of everything can only come from our context within life or existence itself, not from observing it from the outside. I think this was probably the conclusion that he arrived at.