The truth of everything is certified by consciousness. Automatical consciousness is true. We may think that i am awareness plus body, but the problem is, we are limited awareness. What adwita wants to show us is you this awareness you feel you are. That is the unlimited awareness, that itself is bramhan.
Inspired by the 15th chapter of the Ashtavakra Gita, Swami Sarvapriyananda gives a discourse on the nature of the Self.