Nothing is outside of the brackets of the universe.
" Please, construct the primordial generating structure of the Universum based on these three concepts: «Time, as an axiom, is simple time. Just like matter is just matter and action is just action, the three axioms that are the ontology that is the universe.» The "clock" has been moved outside the brackets: there is only Nature and your Mind."
By nature and mind you seem to mean the basic duality of our world, mind and body. I am with you, but that duality still exists inside of the brackets that are the universe. Nothing is outside of the brackets including the clock, which is the quotient of action and matter and that clock is within the universe.
So your "nature" appears to deal with matter, time, and action, which is the trimal of our Cartesian representation while your "mind" deals with a complementary relational representation. The trimal of origin, destiny, and purpose describes the stories that we experience, remember, and tell about the relations of objects and that is how our mind and consciousness works.
There is a dual representation for the universe that roughly corresponds to the perpetual philosophical discourse on dualism. The Cartesian representation is all about the ontology of matter, time, and action, what you call "nature." The relational representation is all about the ontology of origin, destiny, and purpose, which are the stories of consciousness, what you call "mind." These are not two different ontologies or realities but rather these are two representations of the same common reality or ontology.
Notice that I am very careful to leave particular stories out of my ontology. The points, lines, planes, and volumes of Euclidean space and Plato's solids and triangle, these are all stories that help us predict action in space. Since the generating structure of the universe is the action equation that describes the change in matter with time, space then becomes a result of action and not the place where action occurs.
"On my system, the Universum and its "beginning" I regard as the "generating process" of the matter which has the structure. I base the ontological structure of this process, which the hierarchy. And then, when the generating structure is constructed, I "grasp" the nature of time."
The universum that you describe has a "beginning" (an origin), a "generating process" (a purpose), and a "generating structure" (a destiny). These are the stories we tell about our relational reality and from those stories we do indeed "grasp" a Cartesian time as well as matter and action. Of course your "generating process" is both the purpose and the action that results in structures or objects.