As you appear to recognize, you are describing a view of the cosmos known as pantheism. This is a theology that proposes that the universe and God are co-extensive. In a sense, God is the universe and the universe is God. This is an oversimplification, but it is more or less what pantheists such as Hindus and Buddhists believe. We should be very cautious to say what all Hindus believe, but the majority idea seems to be that if we achieve nirvana, then we are absorbed into the universal mind, also known as Brahman. Atman (soul) becomes brahman (universal soul). In a sense the universe is God and we are God.
But you point out, at least indirectly, that pantheism is not consistent with the facts we know about the universe we live in, including the fine tuning of the properties of the universe. If the universe itself is fine-tuned, does that mean that God fine tuned himself? Also, pantheists simply MUST believe that the universe is eternal. In fact, both Buddhists and Hindus have a cosmology of an infinite series of creations and destructions of the universe. Why? Because if the universe is coextensive with the universal soul/God, then God could not create himself and the universe, therefore, must be uncreated and eternal.
The problem with pantheism is that it is wrong! The universe is not eternal. The universe was “created” in an apparent creation event that we call the big bang. At least, that is what all cosmologists have concluded from the data. On the face of it this disproves pantheism, or at least it appears to do so.
Your question is in a sense, backward. You ask if the universe is self-thinking and conscious, then does that prove pantheism. It is the other way around. If pantheism is correct, then it implies that the universe is self-thinking and conscious. This would be a classic circular argument. A better question is this: Are the properties of the universe consistent with a self-thinking, conscious universe? The straightforward answer is no, they are not. The fact that the universe has not always existed, and the fact of the fine tuning of the universe both very strongly argue against pantheism.