I suspect this is a bit more like 'Ask Prehistorians' but here goes anyway. In our early days of developing weapons we as a species came up with a variety of pretty common forms that stayed in use for thousands of years if not up to the current day. Now swords and spears and so forth seem to have an obvious inspiration and progression but the bow rather baffles me.
It seems a reasonably complex thing to come up with from base principles and it leaves me curious if we have examples or indications of how the bow was conceived. Are there proto-bows that showcase humanity toying with the idea and eventually arriving at the core shape and functionality that has been refined upon ever since or, as far as we know, did it just spring into use fully formed?
You're instincts are right that another sub might be helpful: /r/Askanthropology may be able to help.
Before the bow and arrow, many hunters used the atlatl, which included a dart that often had a feathered end to give it stability. The darts typically had a stone spear point that was heavier than that of an arrow. The technology was particularly effective against larger game. That said, the basic idea of the arrow was present in the atlatl/spear thrower.
Bows and arrows were more suited to smaller, post-Pleistocene environments with smaller game. It is a common misconception that people of the past were surrounded by "primitive" technology because they were not "advanced" enough or they were not as bright as we are. In fact, hunter-gatherers were extremely sophisticated, and when they were confronted by a changing environment, they adapted with new approaches that suited new challenges. We cannot know who or when the first person used a bow rather than an atlatl to deliver a stone point on the end of a dart, but it isn't really a gigantic leap.
We don't see any progression from proto-bows to bows - our earliest sure evidence of archery is fully-developed bows (and earlier possible evidence is small stone points, which could have been arrowheads, but we don't know how the projectiles were projected).
There are, however, 3 possible proto-bows. Two are very bow-like; what we don't know is whether they developed from bows, or whether bows might have developed from them. One bow-like possible proto-bow is the musical bow, essentially a one-stringed musical instrument, sometimes with a resonator attached, and sometimes with the player's mouth used as a resonator. See Camp, C., & Nettl, B. (1955), "The Musical Bow in Southern Africa", Anthropos, 50(1/3), 65-80, https://www.jstor.org/stable/40451020 for descriptions of such instruments. The instrument can be played by plucking the string or by striking the string with a stick. There is rock art showing a possible musical bow that is older than any clear depiction of the bow-and-arrow or any surviving bow: http://www.ancientlyre.com/images/trois_freres3_n.jpg (image from http://www.ancientlyre.com/the_incredible_survival_of_the_harps__lyres_of_antiquity_in_africa_today/ which also links video of musical bows in use).
The other bow-like possible proto-bow is the bow-drill, likely having seen earliest use as a fire-drill, and used later as a drill for making holes.
Less bow-like, but importantly using the elasticity of wood, and therefore a possible ancestor, is the spring pole trap. There are various versions of such traps, e.g., https://en.wikipedia.org/wiki/Deadfalls_and_Snares#/media/File:SnareSpringPole.jpg which often use a sapling as the spring.
If the spring pole trap is an ancestor of the bow, the line of descent might be through the musical bow. The African ground-bow or earth-bow is another one-stringed musical instrument (and possibly the ancestor of the skiffle bass/washtub bass/teachest bass), with one end of the string attached to a bent stick/sapling. Make the ground-bow portable by attached the string to both ends of a bent stick, and you have the musical bow. An African ground-bow in action: https://www.youtube.com/watch?v=DQeEtvUkulA
