What is the source of His existence? How did they come to know about Him.
Anybody who is a yogi (see Gita) can know Brahman. Understanding Brahman and its identity with the Self (Atman) is the major topic of the Upanisads. The scripture below should clear all your questions about Brahman and Atman.
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Brihadaryanaka Chapter 4 (Yajnavalkya writes)
Regarding this there are the following verses:-
There is an ancient path
Extremely fine and extending far;
It has touched me, I've discovered it!
By it they ascend to the heavenly world
Released from here,wise men, knowers of Brahman.
In it are the white and the blue, they say,
the orange, green and red,
By Brahman was this path discovered;
By it goes the knowers of brahman,
The doers of good, the men of light.
Into blinding darkness enter those
who worship ignorance;
into a greater darkness than that, as it were, enter
those who are delight in learning alone.
‘Cheerless indeed are those worlds covered with blinding darkness.
To them after death go those people who are ignorant and unwise.’
If a person truly perceives the self.
Knowing, "I am He".
What possibly could he want,
Whom possibly could he love,
That he should worry about the body?
The Self has entered this body, this sense jumble;
If a man finds him,
Recognizes him,
He's the maker of everything- the author of all!
The world is his - he is the world itself!
While we are still here, we have come to know it.
If you've not know it, great is your destruction.
Those who have known it - they become immortal.
As for the rest - only suffering awaits.
When a man clearly see this Self as God,
the Lord of what was
and what will be,
He will not seek to hide from him.
Beneath which the year revolves
together with its days,
That the gods venerate
as the light of lights,
as life immortal.
In which are established
the various groups of five (the senses),
together with Space;
I take that to be the Self-
I who have knowledge,
I who am immortal,
I take that to be-
the Brahman
the Immortal.
The breathing behind the breathing,
The sight behind the sight,
the hearing behind the hearing,
The thinking behind the thinking-
Those who know this perceive Brahman,
the first,
the ancient.
With mind alone must one behold it-
there is nothing diverse at all!
From death to death he goes, who sees here
Any kind of diversity.
As just singular must one behold it-
Immeasurable and immovable.
The Self is spotless and beyond space,
Unborn, immense, immovable.
By knowing that very one a wise Brahmin
should obtain insight for himself.
Let him not ponder over a lot of words;
It just tires the voice!
This immense unborn self is none other than the one consisting of perception here among the vital breath.
There in that space within the heart, he lies- controller of all, lord of all, ruler of all!
He does not become more by good actions or in any way less by bad actions.
He is the lord of all! He is the ruler of all creatures! He is the guardian of all creatures!
He is the dike separating the these worlds to preserve theirdistinctions.
It is he that Brahmins seek to know by reciting the Vedas, sacrifice, gift-giving, austerity and fasting.
It is he, on knowing whom a man becomes a sage.
It is when they desire him as their world that wondering ascetics undertake their asceticism.
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