There is no date we know of nor could it be reasonably narrowed down.
What we know is that the Chinese developed black powder in the 10th century and the fire-lance and hand cannon in the 13th. Middle Eastern culture acquired the technology in the 14th century, followed closely by the Europeans. Arab alchemists refined the black powder recipe to near perfect explosive potential. Europeans developed gun technology through the harquebus, blunderbuss, musket, and finally the rifled barrel, and projectile technology from scatter-shot, ball shot, ball slugs, minieball, through to modern bullet/ball configurations.
Likely as not, firearms were used for hunting from the first military deployment. Early armies relied on hunting and gathering to feed the troops.
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The first gun was used for hunting in 1260 after the Chinese had invented gunpowder in the 9th century. These inventions were later transmitted to the Middle East, Europe, and Africa.
The bow was invented in the late Paleolithic Era (around 10,000 to 9,000 BCE).
Apex - About 50,000 years