Throughout the Book of Mormon, there is evidence that there were no standing armies. This is the way that many ancient cultures worked, and specifically those in Mesoamerica where many scholars would place the Book of Mormon events. Therefore, it isn’t surprising that when hostilities erupted, each side was quickly armed. In many cases, the arms were simply repurposed hunting weapons, but it was also probable that many men would have military weapons available in the chance that they were called to defend their lands.
Thus, there was no need to call up armies, because there were no armies. Those who decided to fight simply picked up their weapons and gathered together with those who were of a like mind. Note that it is not until the Nephites are preparing to meet the Amlicites that they appoint captains and higher captains. There was no standing army which already had those positions filled.