Though the brain has had a center of importance since at least 17 BCE in Egyptian papyrus (discovered by Edwin Smith), it's role in human conscious wasn't really widely discussed or accepted until the Greeks started pondering the use of the brain as outlined by the Pythagorean Alcmaeon of Croton in the 6th and 5th centuries BCE.

These proposed that the brain was the center of cognitive function, but as the "doctors" of the time thought the body sacred, this was more philosophical rather than based on empirically gathered evidence from anatomy.

Of course, most people know that we really cemented our thoughts on the brain and its function through battles and most recently Phineas Gage's condition has become centered in popular culture, but the ancients believed that the soul/consciousness/self's location varied.

To some, what we think of as the function of the brain was found in the heart (Egyptians, others), Liver (Americas), Renal (Mediterranean), etc. Speaking of the heart, Minds Behind the Brain: A History of the Pioneers and Their Discoveries By Stanley Finger goes into detail as to how the perception of cognition and soul have been linked to other organs and even external location of what we think of as personality.

As a historical archaeologist, I am familiar with the field of Neuroanthropology which is essentially how the brain and cognition is linked to cultural development. This is only loosely relevant, but it informed my statements above and further research to familiarize myself.

I've written answers to two similar, related questions recently: How did the idea that the heart is the source of emotion develop? and When and how did it become common knowledge that the head/brain is the seat of thought?, which between them should help answer your question!