The size of the Homo brain can be attributed to the style of infant development. Most of the growth of the brain in monkeys and apes occurs before birth with little additional growth after. In humans growth of the brain continues to grow rapidly after birth for about the first year. Within one year a baby human has about twice the brain capacity as a chimpanzee. This pattern of brain growth in humans is a reflection of the delayed maturation cycle in humans.
Humans mature much slower than do other primates.
Remember our baby teeth are not replaced with permanent teeth until we are much older. This delayed maturation is more than offset by the increased intelligence associated with a larger brain capacity. The human intelligence is able to deal with a variety of environmental problems because the greater intelligence. Humans are neither strong or fast but have come to dominate the Earth. It may not be hard to understand why it took over 1.5 million years for Humans to evolve after the appearance of the Australopithecus.