I think MB already addressed this by reference to Zen but I don't think most people will understand the reference.
Mahayana Buddhism, practiced in most east asian countries, stipulates that in order to understand being you have to transcend the concepts and constructs that create your reality. There's no way to do this except to experience it. The best we can do with language is force you to contemplate things that are absurd or internally contradictory such as the famous 'one hand clapping' koan.
You can refer to this "place" beyond concept, logic, reason, etc as being absurd territory and in some sense you'd be right. But the point is that in order to know what it really means to exist, you need to transcend your own existence.
Nice. The problem as I see it lies in language and the emotional impact we can have on children with words, put downs specifically. We were born perfect because we could not compare ourselves to anything. We did not use words or name things, could not think using language to represent ideas. We were born with a huge plasticity of potential and massive being joy, only to be crammed into some particular ego identity. We were controlled and forced to conform to local standards by being made to experience the terror of the denial of love if we wondered too far from the farm.
We learned about things that have no reality at all, like good and evil. If we strayed from the safety of proper behavior we were told we are evil and worthy of our own self contempt. We were cast from the garden of Eden where no evil existed, our perfect original stat, a state that will reappear when the delusions of self hate disappear. Thought is the carrier of these delusions, the belief in ideas, the notion, say, that evil actually exists.
Thought is time. Thought is memory of the past, the absorption of concepts and ideas to which painful experiences cling. Though creates time. Time disappears when thought ends. The purpose of the Zen koan is to end time. When time ends one enters the immortality of being. There is the delusions of time that create the ego, and the state of infinite being.
So I would say, then, that to know what it means to exist you have to cease to exist completely. What we mean by existence is a delusion of the ego.
In order to be you have only to end time and enter the now. And have we really ever been anywhere else?
As the Zen master says, 'Everybody is enlightened. It would be nice to know it'.