According to Advaita Siddhanta, Brahman is said to be the only reality, all else being but an illusion due to avidya (ignorance). As per Hindu teaching, Brahman is self luminous, pure consciousness. So, the Brahman is svayam siddha (self established), both epistemologically and ontologically.
Epistemologically, it can never be the object of empirical knowledge, that is, it cannot be proved on any basis. It is underlying basis that the knower-subject for the very operation of the sources of knowledge and hence it cannot be known through them.
If it is to become the object of an experience, this would involve a subject-object distinction within itself, which is a product of ignorance. Further, this would lead to infinite regress, as one would have to accept another consciousness (as the ‘knower’) to cognize it as an object, and so on.
Ontologically, Brahman is identified with one’s inner Self. It is permanent and is constantly affirmed by the notion ‘I am’. This notion can never be denied and requires no proof. It cannot be doubted, since it is the very self of one who doubts and is always present even in the act of doubting or denial of its existence. No one can assert without contradiction that He does not exist.
The self, being the first cause, is not a modification or an effect. If it were so, it would lead to the doctrine of the void or nihilism. Thus, Brahman is self-established as eternal, constant, above all change, and not dependent upon any external cause or means of proof.