Archaeology student here. I suspect that the atlatl developed from the use of slings to propel stones in hunting small game. Most contemporary hunter gatherer groups utilize stone slinging pouches of some kind to very accurately and lethally hurl lump projectiles (think the Biblical example of David and Goliath, with the former using a leather pocket sling to deliver the fatal conk on the head to the big guy). Such slings have been found in sites occupied by Pleistocene era peoples so we know how they were used.
It isn’t much of a step to translate that over the shoulder forward flinging launch action into a device for hurling a linear projectile, probably a dart at first and eventually a longer simple spear and then a blade- or harpoon-hafted spear.
It has long been a fact of human intelligence that there are individuals born with a natural ability to analyze actions and engineer tools to enhance them to improve the odds of survival. That inherent creativity and behavioral adaptability is homo sapiens’ major distinction from the rest of the animal kingdom. Combined with our being able to develop language so that we could share inventions with others of our tribe enabled our puny, otherwise defenseless naked selves to survive and spread across every corner of the planet in less than 70,000 years.
Those talents are both a blessing and a curse since our abilities to share and rapidly build on and innovate technologies have lead to our species dominating the planet and consuming its resources at an unsustainable pace.