How long was the us an independent nation when it found itself internally divided and at war with itself?

The United States became an independent Nation on September 3, 1783, with the Treaty of Paris.

It found itself divided when, on December 20, 1860, South Carolina seceded, followed by Mississippi (January 9th 1861), Florida (January 10th), Alabama (January 11th), Georgia (January 19th), Louisiana, (January 26th), Texas (February 1st), leading to the foundation of The Confederate State of America (CSA).

It found itself at war on April 12, 1861, after the bombardment of Fort Sumter, which led Virginia (April 17th), Arkansas (May 6th), Tennessee (May 7th), North Carolina, May 20th), to join the Confederacy.