Manduka Upanishad, Brahman and Atman are defined as the same.+

Atman is Brahman (God in truth), the One without A Second.

In Manduka Upanishad, Brahman and Atman are defined as the same:~ sarvam hyetad brahmaayamaatmaa brahm soyamaatmaa chatushpaat –

Manduka Upanishad, verse-2

All indeed is this Brahman; This Atman is Brahman; God, this Atman has four steps/quarters.

While Brahman lies behind the sum total of the objective universe, some human minds boggle at any attempt to explain it with only the tools provided by reason. Brahman is beyond the senses, beyond the mind, beyond intelligence, beyond imagination.

Indeed, the highest idea is that Brahman is beyond both existence and non-existence, transcending and including time, causation, and space, and thus can never be known in the same material sense as one traditionally 'understands' a given concept or object.

The Atman is Self-evident. It is not established by extraneous proofs. It is not possible to deny the Atman, because it is the very essence of the one who denies it. The Atman is the basis of all kinds of knowledge, presuppositions, and proofs.

The Soul, which is present in the form of consciousness, is real and eternal. The world in which we exist is an illusion created out of consciousness.

Rig Veda: ~ The Atman (Soul or Spirit) is the cause; Atman is the support of all that exists in this universe. May ye never turn away from the Atman, the ‘Self’. May ye never accept another God in place of the Atman nor worship other than the Atman?" (10:48, 5)

Brihadaranyaka Upanishad: ~ Brahman (God) is the form of the Athma, and it is indeed Athma itself.

Sage Sankara’s Supreme Brahman (God) is impersonal, Nirguna (without Gunas or attributes), Nirakara (formless), Nirvisesha (without special characteristics), immutable, eternal, and Akarta (non-agent). It is above all needs and desires. It is always the Witnessing Subject. It can never become an object as it is beyond the reach of the senses. Brahman is non-dual, one without a second. It has no other beside it. It is destitute of difference, either external or internal. Brahman cannot be described, because description implies distinction. Brahman cannot be distinguished from any other than It. In Brahman, there is no distinction of substance and attribute. Sat-Chit-Ananda constitute the very essence or Svarupa of Brahman, and not just its attributes. The Nirguna Brahman of Sage Sankara is impersonal

Thus, it refers to a formless and attributeless God, which is the Atman (Soul), the ‘Self’ within the false experience. Thus, it indicates clearly that all the Gods with form and attributes are mere imagination based on the false ‘Self’. Thus, Atman or the invisible Soul, the Self, is God.

Sage Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as the Brahman. He brought out the identity of the Self with consciousness and made the Atman the Brahman. Since one will not negate the existence of his Self, he will accept the existence of the Brahman, which is the Atman or Soul, the Self. Both Buddha and Sage Sankara kept silent about the absolutely unimaginable God. The same philosophy was dealt with by them in different angles in different situations.

Sage Sankara not only proved the existence of God from the Vedic perspective but also proved the existence of God rationally by pure reason.

Sage Sankara himself had often said that his philosophy was based on Sruti, or revealed scripture. This may be because Sage Sankara addressed the ordinary man, who finds security in the idea of causality and thus, in the idea of God, and Revelation is indispensable to prove the latter. He believed that those of superior intelligence have no need of this idea of divine causality and can therefore dispense with Sruti and arrive at the truth of Non-Dualism by pure reason.: ~ Santthosh Kumaar