The "I am" experience is "proof", so to speak, of existence.
This phenomenon of existence alone is beyond our ability to comprehend even remotely close to completely.
Because we can't remotely comprehend it all, we are left to conclude, logically, that there is more to existence than we can comprehend.
But our need to comprehend at times causes us to speculate to fill in the gaps.
Religions can result.
That's not to say that God does not exist, as not only are God and religion not mutually inclusive in some such speculations, but existence is such a difficult experience to grasp in all its incredible awesome facets, that when we begin to ponder what it would be like should we suddenly cease to exist .. well, it's difficult to comprehend that all would be lost, our self as well. Something, or someone must keep it all going.
I find it interesting that we have a tendency to create God in a way that we can comprehend and manage to relieve us of the terror that comes from the speculation of death.
Some say that we're not just creating God in our own image, but that God is providing us with a glimpse we can handle, each of us having a different though sometimes compatible glimpse.
Regardless, if two people sit in a room, they can both look at each other and say, "I am, and no one else is me." Each experiences only their own self. So if I, all my life, have been just me, each person I meet has experienced the same thing, logically, the experience of being a "me" distinct and apart from my own self .. but I can't experience them as a "me" -- only they can experience that, and, they do.
That can be mind-boggling, that my "I am" is isolated, so to speak, from everyone else's same experience, and that I have always been only me, sometimes such that it's almost as if no one else exists but me .. even though they do.
How can that be? It is .. .. but, how, how can that be?
And each one of us experiences the universe, and we do so as if we were at the the very center of it all, at the very dynamic middle between our macrocosm and our microcosm of all that is.
All this can tell me that being alive is not just limited to me, that others, too, are alive and experience this awesome existence from an alone "I am" place, of which I am an integral part.
My awareness of the vastness of the universe I perceive causes me to logically speculate that such "I am" beings may exist elsewhere, outside and inside me.
My perception of the universe I conceive of, taking it as a whole, makes me ponder beyond my capabilities, how can this all exist and why and by what means?
Maybe I'm a composition of all that is outside me and all that is inside me merging into a singularity, a dynamic living singularity created from all, from all that is, from all that is alive in its own way.
And how has this all come about?
Just because God is a natural conclusion doesn't mean God is merely only a creation of our own speculative facilities.
Sometimes, yes, we speculate what later appears as falsely.
But sometimes we speculate truly, whether we know it or not ..
.. And such speculation might also be a form of communication.
So God simply might be the name of the universe, the ultimate "I am" ..
.. Or much, much more.
But something as our universe we're just beginning to grasp, something so infinitely immense in all its aspects, .. well, how could something like that exist, simply exist without being created, created by something .. or some "one".
I believe that our speculation can be a form of communication, received and engrained upon us.
The very fact that I can merge with another "I am" and create a third "I am", that alone, may be sufficient "proof", both logically and emotionally, that such a creator, God, exists.