Sage Sankara proved the existence of God by declaring ~ Atman is the only one ultimate reality or Brahman or God in truth.+

Sage Sankara proved the existence of God by declaring ~ that Atman is the only one ultimate reality or Brahman or God in truth.

The proof of God’s existence is not possible without knowing what God is supposed to be in actuality. God is existence itself.

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

Sage Sankara himself had often said that his philosophy was based on Shruti, 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 for this idea of divine causality, and can, therefore, dispense with Shruti and arrive at the truth of Non-Dualism by pure reason.

When Sage Sankara says Brahman or God is impersonal and attributeless then why worship God with form, names, and attributes.

God and Goddess are religious concepts. Whatever is seen, known, believed, and experienced as a person within the dualistic illusion (world) is a falsehood.

Sage Sri, Sankara’s Supreme Brahman (God in truth) 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 besides it. It is destitute of difference, either external or internal. Brahman cannot be described because description implies a distinction. Brahman cannot be distinguished from any other than it. In Brahman, there is not a distinction between substance and attribute. Awareness constitutes the very essence or the true nature of Brahman, and not just its attributes. The attributeless Brahman of Sage  Sankara is impersonal.

When Sage Sankara says Atman is Brahman or God then why believe and accept anything as God other than the Atman. Vedas say May ye never turn away from the Atman the innermost self. May ye never accept another God in place of the Atman nor worship other than the Atman?

~ Then, why worship non-Vedic Gods in place of Atman, the real God.

Self-realization is the truth- realization. Truth- realization is God-realization and God-realization is real worship.

Lord Krishna says Ch ~V: ~ “Those who know the Self in truth.". The last two words (tattvataha) are usually ignored by pundits, but they make all the difference between the ordinary concept of God and the truth about God. One must realize the difference between the ordinary concept of God and the truth about God.

Religious Gods are based on blind beliefs. Religious God cannot be considered as the center because the Soul the  ‘Self’ is the center of all that exists. 

Without the Soul, the world in which you exist ceases to exist, which means the religious God is dependent on the Soul for his existence.

Even Rig Veda: ~ The Atman 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)

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

Sage Sankara is the only Sage who proved the existence of God by declaring ~ that Atman is the only one ultimate reality or Brahman. Brahman is God.

Atman is Brahman. The Atman is the Self is non-dual because there is no second thing that exists other than the Atman. Atman is present in the form of consciousness. Consciousness is the only true reality, and everything else, that appears as form, time, and space is merely an illusion.

Advaita means the Soul, the Self, which is second to none. The Soul, which is present in the form of the Spirit or consciousness, is the ultimate truth or Brahman or God in truth. 

Advaita is the nondual nature of Atman, which is God in truth. Advaita is God. Advaita is the fullness of consciousness.

The Soul, the Self itself is Brahman or God in truth. God in truth is present in the form of consciousness. 

God in truth is ever-present. Without consciousnesses, which is God in truth, the world, in which you exist, ceases to exist. God is self-evident. God in truth is not established by extraneous proofs. It is not possible to deny the existence of God in truth because it is the very essence of the one who denies it. God in truth is the basis of all kinds of knowledge, presuppositions, and proofs. God in truth is everything.  

God in truth which is present in the form of consciousness, is the ultimate truth or Brahman.

 Bhagavad Gita says: ~ Brahmano hi pratisthaham ~ Brahman (God) is considered the all-pervading consciousness, which is the basis of all the animate and inanimate entities and material. (14.27).

When Bhagavad Gita says, that God is considered the all-pervading consciousness which is the basis of all the animate and inanimate entities and material then nothing has to be accepted as God other than consciousness.

The Soul, the God 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.

God is beyond is hidden by physical existence. God can never be proved, through intellectual argument but God can be realized by getting rid of ignorance. Only by acquiring Self-knowledge or Brahma Gnana or Atma Gnana getting rid of ignorance is possible.: ~Santthosh Kumaar