If there is only one such structure, if it is unique, then the question of its existence goes away. What would existence mean?
We would just know there was a unique self-consistent all consistent form covering structure. And that any form within that structure, with a sophisticating self-sensing self-interpretive ability, would experience its own existence.
Existence would then mean, part of the unique self-consistent, zero-information, independent of any externality, structure.
A perceived existence as a result of a unique tautological structure, not a result of any external composition.
And the phrase "I think therefore I am", would be tautological in both senses. As evidence. But also, as the actual meaning of existence. Given a self-aware form within a tautology, its perception of existence is the nature of existence.
Reality was always going to be something that forms structures, that are somehow inevitable, the only possibility, not something selected or manufactured by something else.