There is possible a realistic as well as an illusionist Advaita. The philosophy of The Life Divine is such a realistic Advaita. The world is a manifestation of the Real and therefore is itself real. The reality is the infinite and eternal Divine, infinite and eternal Being, Consciousness-Force and Bliss.
This Divine by his power has created the world or rather manifested it in his own infinite Being. But here in the material world or at its basis he has hidden himself in what seem to be his opposites, Non-Being, Inconscience and Insentience. This is what we nowadays call the Inconscient which seems to have created the material universe by its inconscient Energy, but this is only an appearance, for we find in the end that all the dispositions of the world can only have been arranged by the working of a supreme secret Intelligence.
The Being which is hidden in what seems to be an inconscient void emerges in the world first in Matter, then in Life, then in Mind and finally as the Spirit. The apparently inconscient Energy which creates is in fact the Consciousness-Force of the Divine and its aspect of consciousness, secret in Matter, begins to emerge in Life, finds something more of itself in Mind and finds its true self in a spiritual consciousness and finally a supramental Consciousness through which we become aware of the Reality, enter into it and unite ourselves with it.
This is what we call evolution which is an evolution of Consciousness and an evolution of the Spirit in things and only outwardly an evolution of species. Thus also, the delight of existence emerges from the original insentience, first in the contrary forms of pleasure and pain, and then has to find itself in the bliss of the Spirit or, as it is called in the Upanishads, the bliss of the Brahman. That is the central idea in the explanation of the universe put forward in The Life Divine.
Rebirth
If evolution is a truth and is not only a physical evolution of species, but an evolution of consciousness, it must be a spiritual and not only a physical fact. In that case, it is the individual who evolves and grows into a more and more developed and perfect consciousness and obviously that cannot be done in the course of a brief single human life. If there is the evolution of a conscious individual, then there must be rebirth. Rebirth is a logical necessity and a spiritual fact of which we can have the experience. Proofs of rebirth, sometimes of an overwhelmingly convincing nature, are not lacking, but as yet they have not been carefully registered and brought together.
Evolution
In my explanation of the universe I have put forward this cardinal fact of a spiritual evolution as the meaning of our existence here. It is a series of ascents from the physical being and consciousness to the vital, the being dominated by the life-self, thence to the mental being realised in the fully developed man and thence into the perfect consciousness which is beyond the mental, into the supramental Consciousness and the supramental being, the Truth-Consciousness which is the integral consciousness of the spiritual being. Mind cannot be our last conscious expression because mind is fundamentally an ignorance seeking for knowledge; it is only the supramental Truth-Consciousness that can bring us the true and whole Self-Knowledge and world-Knowledge; it is through that only that we can get to our true being and the fulfilment of our spiritual evolution.