To clarify, you're asking if Native Americans used bows prior to the arrival of Europeans? Unequivocally yes. A great old thread by /u/Reedstilt covers some of this in detail. The tl;dr is that there were plenty of native woods available that made very good bows, with equivalent power and performance to European bows.

Firearms were the big prized weapon in the North American trade. To simplify things, firearms were used alongside bows throughout the history of Euro-Indian conflict, with different effects in different regions and eras. But even as late at the mid 19th century, bows and arrows were often used for cultural effects - among Apaches and other western plains groups, firing arrows into a wounded or dead enemy often marked a specific act of vengeance. Bows were also used among the army of Sitting Bull in the 1876 campaign that led to the Little Big Horn.