You are on the target. Fish contain high levels of the fatty acid DHA. DHA is the main limiting factor on the growth of the brain, and needed exogenously (AA needed too, but can be converted internally). Humans cannot easily get access to DHA from things like grass. That’s why large herbivores grow in bodymass, but their brain size (encephalizatiom quotient) stays low. Dolphins, who eat primarily fish, have a much more similar brain to us, and one of the highest encephalization quotients...

Due to changes in geography in Africa, proto-humans found themselves along the shorelines with ample supples of fish for the first time. They ate more DHA, which lead to the growth in brain cells (brains are built of these fatty acids). This extra brain power, through the process known as exaptation (the lesser known evolutionary concept to survival of the fittest), is what is theorized to have then opened the door the human creativity, symbols, language, etc.

Basically, our bigger brains were caused by an increase in the previously limiting nutrient, which was then put to to use for advanced traits, not the other way around as this article purports....

That is a TL;DR as don’t have time to write it all out, but have written and presented on this topic...

https://www.wiley.com/en-us/Human+Brain+Evolution%3A+The+Inf...

Edit: this abstract below has a good summary, and book above is great compilation of papers on the topic.

“The circumstances of human brain evolution are of central importance to accounting for human origins, yet are still poorly understood. Human evolution is usually portrayed as having occurred in a hot, dry climate in East Africa where the earliest human ancestors became bipedal and evolved tool-making skills and language while struggling to survive in a wooded or savannah environment. At least three points need to be recognised when constructing concepts of human brain evolution : (1) The human brain cannot develop normally without a reliable supply of several nutrients, notably docosahexaenoic acid, iodine and iron. (2) At term, the human fetus has about 13 % of body weight as fat, a key form of energy insurance supporting brain development that is not found in other primates. (3) The genome of humans and chimpanzees is <1 % different, so if they both evolved in essentially the same habitat, how did the human brain become so much larger, and how was its present-day nutritional vulnerability circumvented during 5-6 million years of hominid evolution ? The abundant presence of fish bones and shellfish remains in many African hominid fossil sites dating to 2 million years ago implies human ancestors commonly inhabited the shores, but this point is usually overlooked in conceptualizing how the human brain evolved. Shellfish, fish and shore-based animals and plants are the richest dietary sources of the key nutrients needed by the brain. Whether on the shores of lakes, marshes, rivers or the sea, the consumption of most shore-based foods requires no specialized skills or tools. The presence of key brain nutrients and a rich energy supply in shore-based foods would have provided the essential metabolic and nutritional support needed to gradually expand the hominid brain. Abundant availability of these foods also provided the time needed to develop and refine proto-human attributes that subsequently formed the basis of language, culture, tool making and hunting. The presence of body fat in human babies appears to be the product of a long period of sedentary, shore-based existence by the line of hominids destined to become humans, and became the unique solution to insuring a back-up fuel supply for the expanding hominid brain. Hence, survival of the fattest (babies) was the key to human brain evolution.”

https://pubmed.ncbi.nlm.nih.gov/16828044/