I often see Native Americans portrayed using a bow and arrow for hunting. You also see the bow and arrow used by various forces throughout history, from the Mongols to the Persian Empire and many more.

Given the relative isolation of the Native American population, after the initial migration across the Bering Straight land bridge, and up until the beginning of European colonization in the new world, where did Native Americans get bows and arrows?

Did they invent bows and arrows completely independently of their invention and use on the Eurasian continent? Or was the bow and arrow something they had access to prior to their migration across the Bering Straight?

When and where was the bow and arrow first invented?

Edit: Mongrels to Mongols.