Final answer:
The first appearance of human-equivalent brain sizes dates back to between 800,000 and 100,000 years ago, escalating from about 600 cm³ to 1400 cm³, corresponding to substantial environmental and technological changes.
Step-by-step explanation:
The first appearance of brain size roughly equivalent to human beings can be traced back to the period between about 800,000 and 100,000 years ago. During this time, there was a rapid increase in brain volume from about 600 cm³ to approximately 1400 cm³. This evolutionary change is believed to have been influenced by the period's rapid climate change, which may have driven the need for larger and more complex brains to survive in an increasingly unpredictable environment. These changes also coincided with significant cultural and technological developments. Other hominid species such as Homo habilis and Homo erectus also exhibited an increase in brain size compared to their primate relatives like chimpanzees.