I am only interested whether you can provide any evidence that Buddha believed that Brahma or any other deity created Reality or whether Buddha gave any explicit theory of Creation..Buddha left the question of Creation and Destruction of Universe open-ended with his 14 Unanswerable Questions...
The closest to a theory of Creation you will get from the Buddha is that this is a steady-state Universe going through endless expansions and contractions-------MahaParinibbana Sutta
Now may be the Hindu theory of the Creation of Universe is true, May be Modern Physic's theory of the Creation of Universe is true, May be Islam's version is true or may be Christianity version is true
So now you have gone beyond your original contention of only limiting the discussion to Vinaya and Sutta Pitaka. That is good.
You are now seeking a false equivalence based on your rather simplistic understanding of Hinduism. In Hinduism, Brahma did not "create" this reality.
Brahma IS the creative force that forms reality. Shiva is the cosmic dust that is put together by this creative force called Brahma. (Hence the roaring child of Brahma). Shakti IS the "Buddhi tatva" (DNA or strength of intelligence) that pushes evolution. Vishnu IS the consciousness that is prevalent all across the cosmos.
Buddha talks about the creation of the Universe in the Digha Nikaya
The Expansion and contraction of the Universe that he talks about is the same as in the Rg Veda and Bahmanda puran. Buddha calls it Abhasara Brahma.
I am ready to accept that Buddha may be a stupid fool who was DEAD wrong about everything, But I will not accept when words are put into his mouth which are not his Original Utterings
We have no idea what his "original uttering" are since Buddha did not write even a SINGLE book. All the books are written by his disciples.
I have no problem if you say Buddha's worldview or approach is faulty...but show me a single evidence that Buddha said that Anatta is a different kind of soul, that the Universe has a Creator, and that whatever is written in the Four Vedas and the first two Upanishads are true
Anatta means no permanent , unchanging soul and it only means that the soul is not part of your body or your mind. Its not part of your "self".
This is the same as in Hindu philosophy where the Atma is not the same as your mind or body.
Universe - creator has already been discussed above.
The only way you can truly know that the Vedas and Upanishads (No idea what you mean by first two) are true is if you yourself reach enlightenment. I cannot "prove" anything to anybody. I can only present Facts.
The closest you will find is that Buddha saying that even Vedic sages didnot proclaim the existence of a Creator..
Now whether that statement is true or not is not my concern, what is of my concern is whether Buddha said that or not
Buddha never commented on the Vedas. His teaching was not about understanding the nature of the cosmos. It was about understanding your true self and discovering the truth for yourself.
His teachings were a user manual to self realization and at worst, a path towards a more dharmic lifestyle.
But when he DID speak, his definition of Brahma, Mahabrahma, Kalpa (life of brahma and the universe) is the same as Hinduism.