IMHO:
I believe that Hinduism descended from Abraham, Avraham Avinu, the Patriarch of the Jews (and incidentally of the Muslims and the Christians). This is neither "my" theory, nor is it a new theory, nor is it supported by mainstream Orthodox Jews. But I like it.
It goes like this:
Genesis 25:1-6:
"Abraham proceeded and took a woman whose name was Keturah. She bore him Zimran, Jokshan, Medan, Midian, Ishbak, and Shuah. Jokshan begot Sheba and Dedan, and the children of Dedan were Ashurim, Letushim, and Leummim. And the children of Midian: Ephah, Epher, Hanoch, Abida, and Elda'ah; all these were the descendants of Keturah. Abraham gave all that he had to Isaac. But to the concubine-children who were Abraham's, Abraham gave gifts; then he sent them away from Isaac his son, while he was still alive, eastward to the land of the east."
Here is the Torah analysis of the above passage:
Our rabbis ask (Miizrachi):
"What gifts did Abrahham have left to give? He had previously given everything he owned to Isaac?"
(Rashi) explains: "according to the Sages (Sanhedrin 91a that gifts are not to be understood in the material sense, but rather) He imparted to them the secrets of the impure or unclean arts."
This refers to the knowledge of demons and sorcery, etc. He imparted this knowledge to teach them to counteract sorcery, and exorcise demons which enter into men (Gur Aryeh)
According to the (HaKsav V'haKabllah), Abraham imparted this knowledge to them so that they would know how to guard themselves from substituting impure names for hallowed names and inadvertently worshipping them.
(Rashi) also adds: another interpretation: Gifts refers to gifts which had been given to him because of Sarah (20:14,16 - Abraham's soujourn in Egypt where Sarah kidnapped by Pharoah), and the gifts he received from others. All of these he now gave to them since he wished to derive no benefit there-from. (Previously he had give Isaac all the wealth he had earned)
He sent them "eastward to the east country." The "land of the east" would have been Charan in Amram Naharaim and Ur Kasdim. These were the lands where Abraham's kin lived and came from. The geographical area that this would have encompassed in modern day terms is Syria, Iraq and even tribal lands in Iran.
He sent his concubine children there, confident that his kinsmen would welcome them and offer them greater friendship than they would have found elsewhere. (Radak)
(Chiizkuni) explains that Abraham sent them there to claim the ancestral inheritance that was due to him for his own family.
Now, according to the Torah, Abraham was renowned throughout the world as the Founder of Monotheism, the belief in the One, True G-d. He had great, great wealth much of it in the form of cattle. Much of the cattle he got on account of Sarahin Egypt, and as gifts from neighboring kings.
Therefore, his concubine children would have gone out as Princes of Abraham; with the knowledge of the G-d of Abraham; with much wealth in cattle; with powers given to them by Abraham to defend themselves against the idol worshippers; to claim their ancestral lands towards the East.
If they were able to claim their lands in the East, they would have become leaders of the Peoples in the lands to the East; the early Persians and Medes
Abraham lived from 1813 BCE to 1638 BCE.
Somewhere between 1700 BCE and 1200 BCE, the Aryan People descended from the Khyber pass and invaded India. They had traveled from the West, first taking over what is now Afghanistan and then moving on to India.
They were a racial mixture of Persians and Medes. They had great herds of cattle. They conquered the Indian civilizations with relative ease. They brought their gods with them into India.
This became the "Dark Ages" of India, but, as with the "Dark Ages" of Europe, it was also a time where new cultures and religions were fashioned. It is called the Vedic Age by the Hindus. Somewhere between 1200 BCE and 600 BCE, the religion of Hinduism came into being.
It was a melding of the new gods of the Aryans and the old animist worship of the Dravidian Indians.
This is what I believe happened:
The children of Abraham became the tribal leaders of the Peoples of the East. They believed in the G-d of Abraham and they knew the Names of all of the Demons and Lesser Powers that could be used to help or afflict man.
They became the Aryan race that migrated East.
As the centuries went by, the G-d
of Abraham became the G-d, Abraham.
This, in turn, eventually became G-d Brahman.
In Hinduism, Brahman is the the "First Cause;" the unmanifested reality of everything.
When it manifests, it is the Creative Force, the deity, Brahma.
The wife of Brahma is Saraswati. In Hinduism, this is the feminine Creator.
Saraswati is a river in India with a minor tributary called Hakara.
Sarah was Abraham's wife. Her slave; his concubine, was Hagar.
The Hindu pantheon - Shiva, Vishnu, Kali, Yama, Krishna, Ganesha, Lakshmi, Agni, just to name of few of the hundreds, if not thousands of Hindu deities, are all considered "Lesser gods." Some are demons. All are aspects of other deities. All are subservient to, or part of, Brahman.
These could have been the names of the Lesser Powers and Demons that Abraham gave his children power over....
In Judaism, there are many Aspects of G-d. And, they all mean specific, different things, but they are all G-d.
We say the G-d of Avraham; the G-d of Yitzach; the G-d of Yaakov; G-d the Father; the G-d of Mercy; the Redeemer; the Creator; the All Supreme G-d; the G-d of Forgiviness; etcetera.
It is all one G-d. There are many Names.
Lastly, in Parshas Lech Lecha, (Genesis 12: 1-3) the Torah proclaims:
Hashem said to Abram, "Get yourself from your country, from your relatives, and from your father's house to the land that I will show you. And I will make of you a great nation; I will bless you, and make your name great, and you shall be a blessing. I will bless those who bless you, and him who curses you I will curse; and all the families of the earth shall bless themselves by you."
My theory would take care of that other one third of humanity that is not Christian or Muslim...
That's my story, and I'm sticking to it.