William J. Hamblin provides evidence for the use of the bow and arrow in the Ancient Near East and Mesoamerica.
William J. Hamblin, “The Bow and Arrow in the Book of Mormon,” in Warfare in the Book of Mormon, ed. Stephen D. Ricks and William J. Hamblin (Provo, UT: Foundation for Ancient Research and Mormon Studies; Salt Lake City: Deseret Book, 1990), 365–99
The distinctive characteristic of missile weapons used in combat is that a warrior throws or propels them to injure enemies at a distance. The great variety of missiles invented during the thousands of years of recorded warfare can be divided into four major technological categories, according to the means of propulsion. The simplest, including javelins and stones, is propelled by unaided human muscles. The second technological category—which uses mechanical devices to multiply, store, and transfer limited human energy, giving missiles greater range and power—includes bows and slings. Beginning in China in the late twelfth century and reaching Western Europe by the fourteenth century, the development of gunpower as a missile propellant created the third category. In the twentieth century, liquid fuels and engines have led to the development of aircraft and modern ballistic missiles, the fourth category. Before gunpowder weapons, all missiles had fundamental limitations on rage and effectiveness due to lack of energy sources other than human muscles and simple mechanical power. The Book of Mormon mentions only early forms of pregunpowder missile weapons.
. . .
At any rate, whichever one of these scenarios or a combination thereof (or some other plausible scenario) proves to be accurate, there is little difficulty in reconciling the descriptions of the use of bows and arrows in the Book of Mormon with the evidence or archery from the cultures of both the Middle East and Mesoamerica.