Im not quite sure what youre asking about here. The US Army has existed nearly continuously since 1775, so the standing army has existed longer than the United States.

The State Militias exist as well, albeit in a slightly modified form. See, in 1916 the US Government reorganized the State Militias into the various state forces, thereafter called the National Guard. These formations, which still exist, are the heirs and direct successors to the state militias.

While Beondthegrave is technically correct in that the State Militias still exist, effectively the state militias were largely in a state of decline from the early 19th century on. The increasing democratization of the American people coupled with challenges to the long standing social hierarchy in the aftermath of the revolution meant that the state militia system was in a dramatic decline and was largely no longer an effective means of national defense. Coupled with this is a dramatic expansion of the United States and the lack of wars against European powers which had dominated most of American history. The wars that the United States would fight in the future were largely on the fringes of the United States where state militia, would have been ineffective. The Mexican-American war would be largely fought by the Regular army and state raised volunteers. The exceptions to this trend were areas of the West where conflict with the native peoples was still a concern, and to an extent in the American South where failed slave rebellions in the 1820's and 1830's coupled with fears Northern extremists in the aftermath of John Brown's raid lead to Southern states to increasingly rearm themselves and organize civilian units.