The ultimate question is not "Does God exist ?" but "Who am I ?". If one can see the answer to this question properly (even though one may not be able to express it using words) then that is Nirvana, Moksha or enlightenment.

One may or may not use God or religion to achieve that end.

The word Brahma (masculine) refers to one of the trimurti : the figure that represents creation, awareness and intelligence. This is to be differentiated from Brahman (neuter gender) which means the Absolute and Infinite reality (in existence, consciousness and bliss). The 3 divine figures of trimurti are the aspects of Brahman in qualitative terms : Brahma (sattwa guna) Vishnu (rajas guna) and Shiva (tamas guna).

Buddhist missionaries were present all over central Asia and in Asia minor. The Greeks knew about them, and so did the Egyptians. There was a port in the red sea with which south Indians were trading extensively, in spices etc.. All this is recorded history..

It is also known that Vikings were working as traders and soldiers in the Byzantium. In fact, the Varangian guard was the most feared and respected of all soldiers. It then becomes very likely that some of these soldiers have encountered a Buddhist / Yogic immigrants in Egypt or Asia minor. And they could have carried this flame further up north to Norway, where there could have been a small camp for meditation hippies. :)

It is wrong to say that Yoga comes out of Vedanta. That'd be very ridiculous indeed. In fact, the 6 classical traditions of Indian philosophy are Samkhya, Yoga, Nyaya, Vaiseshika, Mimamsa and Vedanta. As you see, Vedanta is very different from Yoga. Both of their paths have overlapped for a while, especially within the Bhagavata religion (which produced the Bhagavad Gita) but they were quite distinct religions for most of the time.

In fact, there exists a pairing of philosophies. And it is like this : Yoga with Sāmkhya, Vaiseshika with Nyaya, and Vedanta with Mimamsa.

Of all these philosophical systems, Sāmkhya is considered the oldest. And its influence can be felt in every other system. Its founder Kapila is admired and respected by one and all. Most importantly, what he said is atheistic !! I have tried to explain the Sāmkhya system in layman's terms in my blog. Please take a look at it, understanding this properly is essential to understanding any other Indian religion or philosophy. Yoga (which can be easily interchanged with the word Tantra) has just taken the philosophy of Sāmkhya and translated it into a theistic viewpoint, and made it into a practical system of life for everyone.

If you want to see how closely Tantra influenced the Vedic tradition, look no beyond than Kashmiri Shaivism.

Vedic or Brahmanic tradition is not against women or the lower castes. In fact, if you look at the number of women who are found debating in the Upanishads, it is very high ! Probably, the most important of the Upanishads - Brihadaranyaka is a series of conversations between Yajnavalkya and his wife Maitreyi. Then we have sages who were born into familes of very lowly occupations : both Valmiki who composed Ramayana and Vyasa who composed Mahabharata and who compiled the Vedas were born into very low castes, and even mentioned to be of dark skin colour !

If at all an Aryan invasion has happened in India, it was more a series of immigrants coming down to settle down in a culturally and technologically superior land. Not much unlike how Indians and Chinese students flock to the US universities today.

The Vedas and Tantra come from the same single root, and that root has its origin in the Indus valley civilization. And it is from that root that Indian mathematics and science germinated.

You are correct in pointing out that Yoga is related directly to Tantra and Sāmkhya. In the Indian tradition, Sāmkhya represents one of the 6 classical philosophical views (darshanas). In fact, it is considered to be the oldest, and its influence can be felt in every other philosophical treatise, including the Upanishads. Even epics like Ramayana and Mahabharata mention Sāmkhya liberally. If there is a single root from which the various million philosophical ideas and religions of India germinate, that would be Sāmkhya.

Now, Sāmkhya literally means "enumeration" in Sanskrit, and its philosophy is tied to enumerating every object in nature with respect to causal relationships. To understand it properly, one has to use the completely non-intuitive system of enumeration that was developed in India - through the use of zeroes.

The 3 gunas of Sāmkhya stand for 3 choices that a finite number has on the axis of integers : to increase (rajas), to reduce to a zero (sattwa) and to stay the same (tamas). These 3 choices are very non-intuitive, especially that of sattwa (becoming zero) which paradoxically is the best bet towards reaching to infinity. The trimurti (literally, 3 forms) pantheon of Hindu gods are just a representation of infinity with respect to the 3 qualities : Brahma (sattwa), Vishnu (rajas) and Shiva (tamas).

So, Shiva is not a human being, but a representation of the cosmos ! He is indeed a historical personality, but only with respect to cosmic history (or the history of the very universe). This is because Indian tradition says that in the beginning, there was neither being nor non-being. And the very first being to have arose from this state of utter neutrality is Shiva. This is what makes him the very first Yogi.

About the human tradition of the Yogic system and its origins, we have to look for Sāmkhya. The meditation seal of Mohenzo Daro gives one possible upper limit to the date of origin. It is from Sāmkhya that both the Vedic and Tantric traditions have arose. From the same source, they diverged into two rivers, which again split into a million more. This is how things work in India : from one, many.. unlike in the USA where it is from many, one.