Both Bhagavan Buddha and Sage Sankara kept silent about the absolute unimaginable God.+

The word Brahman means ultimate truth or reality which cannot be indicated by any word. The Brahman can be expressed through silence because it is beyond the experience of form, time, and space.  Therefore, the word Brahma clearly stands for the essence of the three states, which is consciousness only. The final use of pursuit of the truth is to know that the  'Self' is the Soul, which is present in the form of consciousness.

Sage Sankara opposed the Buddhists only, who misunderstood Bhagavan Buddha and became atheists. According to Sage Sankara meditation always means a critical analysis of the 'Self' to get salvation from worldly tensions. Due to the eccentric ego of the then atheists, Sage Sankara did not go beyond this since the atheists will not accept God beyond themselves. This limitation is not due to limited knowledge of Sage Sankara but is due to the then-existing situation of the psychology of the surrounding society. 

Even Bhagavan Buddha kept silent about God because the society dealt by Him consisted of Purvamimamsakas, who were strong atheists. Bhagavan Buddha said everything,  including the Delf, is only relatively real (Sunya). This is correct because the self is a part of the universe, which is relatively real with respect to the absolute unimaginable God. The Bhagavan Buddha stopped at this point because the atheists cannot realize the existence of the unimaginable God indicated through His silence. 

The point of Bhagavan Buddha is that if God is non-existent, the entire creation,  including the Self is non-existent. Sage Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as Brahman. He brought out the identity of 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 innermost self. Both Bhagavan Buddha and Sage  Sankara kept silent about the absolute unimaginable God. The same philosophy was dealt with by them from different angles in different situations. 

Remember:~

Buddhism has no answer to certain questions like the existence of Atama [Soul] and rebirth.

Dalai Lama said: Buddhism need not be the best religion though it is most scientific and religion and inquisitive. But Buddhism has no answer to certain questions like the existence of Atama [soul] and rebirth. Dali Lama said that as an individual he believes in rebirth as he had come across a few cases of rebirth. Modern science, Dalai Lama hoped would unearth the mystery behind the rebirth. (In DH –dec-212009-Gulbarga).

In the same way, all religions of the world and all philosophies of the world are based on individuality (ego) find no answers to many questions. Truth seekers all over the world are trying to find answers for themselves, and they imagine and write articles and books on their ideas and others will read and blindly accept them as the ultimate truth.

There is no need to condemn anyone's’ views and ideas or writing, but without being judgmental, the seeker has to verify whether the author is speaking from the standpoint of ego, or whether he is speaking from the standpoint of the Soul, the Self. If his views are based on the standpoint of the physical self (ego), then there are many doubts and confusion. If his views are based on the Soul, the Self then there is no confusion and doubts of any sort.

Nothing has to be accepted without verifying the validity of any claim in the pursuit of truth. Only uncontradictable truth has to be accepted as the truth. There is no need to condemn any religion or any saints or sages, but the seeker has to think beyond religion, scriptures, and individualized Gods.

It is difficult to understand assimilate within a framework of some teaching or holding some philosophy as a yardstick. We have to drop all our accumulated dross to understand and assimilate and realize the Advaitic truth. I am highlighting some scriptural citations only to show the seeker that the Advaitic Sages themselves declare that scriptures, religion, and ideas of God are unimportant in the pursuit of truth. It is easier to understand, assimilate and realize the ultimate truth or non-dualistic truth by rationalizing our views and understanding:-

There is only the mind which is present in the form of the universe. Thus, we have to investigate the world that confronts us.

Consciousness is that which knows everything, that which sees. Consciousness alone remains after one gets rid of all thoughts and ideas by identification with the Soul, the innermost Self. The consciousness is only the seer; it is not Brahman that is an error. It becomes Brahman only after the soulcentric reasoning. : ~ Santthosh Kumaar