OM Asato ma sad gamaya, tamaso ma jyotir gamaya, mrityor ma aamritaam gamaya. Shanti, Shanti, Shanti.+*****

The seeker's aim is the search for the Ultimate Truth or Brahman, the search to find the non-dualistic truth that in actuality never was lost, only hidden.

Upanishad aspiration is best expressed in the following sutra:~

OM Asato ma sad gamaya, tamaso ma jyotir gamaya, mrityor ma aamritaam gamaya. Shanti, Shanti, Shanti

"OM Lead me from ignorance to truth, from darkness to light, from death to immortality. Peace, Peace, Peace" (Brhadaranyaka Upanishad (1/3/28)).

The belief system was coherent because they had a transcendent God as a central doctrine, whereas on the non-dualistic perspective god cannot be considered as the center. 

First, one should not hold a God as the center of existence without verification. Both the theist and atheist are theories nothing to do with ultimate truth or Brahman. 

The belief of God is not God. Holding a belief as God is holding an illusion as reality because the belief is possible only within the realm of duality. Duality is merely an illusion from the ultimate standpoint.  Without the belief of God, the belief system holds no water.  Belief is not God. Belief needs a believer.  The believer needs to be born in this world. If the believer is born than he is part of the illusion.   

Without the believer, there is no belief.  The believer and his world and his belief of GOD are part of the illusion because the self is birth-less because the self is formless. The one, which is born, lives and dies, is not the self.    The Soul, the Self is formless substance and witness of the falsehood (universe or waking or illusion), which is soul or consciousness, consciousness is the ultimate truth or Brahman or God.  

The seeker has to become aware of the existence of the formless witness apart from the three states. The formless witness is the soul, the innermost self, which witnesses the coming and going of the three states. 

The seeker  has to indulge in deeper self-search  to realize  the fact that,  the self is neither the waking entity(you)  nor the self is the dream entity,  but the self is formless soul, which witnesses the coming and going of the three states, in succession. 

This truth  has to be mentally grasped and assimilated to realize the formless Soul, the self is nothing to do with the three states. From the standpoint of the formless Soul, the Self, the three states are mere illusion. 

Till you realize you and your world are made of the same stuff.  And that stuff is Soul, which is present in the form of consciousness.    The Soul, the Self remains in the web of the form, time and space. When the Soul wakes up in its own awareness, the illusory form, time and space, become one with the nature of the soul. Thus, in Self-awareness, there nor you, nor me, nor others,  nor the world, because there is unity in diversity. That is oneness in the midst of the dualistic illusion or Maya.  

Thus, you have to realize the fact that, the whole universe in which you exist is made of the single stuff is very much necessary to realize the Advaitic truth, which is beyond the form time and space.

The mind becomes still when ignorance vanishes. The ignorance vanishes, when wisdom dawns. When wisdom dawns, then the soul, the innermost self, remains in its own awareness in the midst of the duality. : ~ Santthosh Kumaar