It's a cool story. I think the naturalistic real-world story of our evolution is cooler. I'm no expert but here's my understanding of our increase in brain power, in broad-strokes:

• our ape ancestors started using tools,
• they started using fire, cooking food, and using language,
• they started formalizing culture, art, and hunting techniques,
• they started having tribal warfare,
• they became us.

The biological evolution stops there, in the sense that we are still that species we were 100's of thousands, maybe millions of years ago. In terms of the second transformation of the movie, it's arguably within sight. The story of that would be:

• Neolithic Revolution (12,500 years ago)
• Bronze Age (5,000 years ago)
• Iron Age (3,000 years ago)
• Aristotelian physics and Euclid's Elements (2,300 years ago)
• the Copernican and Scientific revolutions (400 years ago)
• the enlightenment (350 years ago)
• the industrial revolution (200 years ago)
• On the Origin of Species (1859)
• maxwell's equations (1862)
• general relativity (1915)
• quantum mechanics (1927)
• the transistor (1947)
• the green revolution (1960)
• the Standard Model (1967)
• manned moon landings (1969)
• the microprocessor#Microprocessors) (1971)
• first complete genomic sequencing (1984)
• the World Wide Web (1990)
• reusable orbital launch systems (2015)