My feeble understanding is that he did not. Bottom of his class at West Point.
George Armstrong Custer (December 5, 1839 – June 25, 1876) was a United States Army officer and cavalry commander in the American Civil War and the Indian Wars. At the start of the Civil War, Custer was a cadet at the United States Military Academy at West Point, and his class's graduation was accelerated so that they could enter the war. Custer graduated last in his class and served at the First Battle of Bull Run as a staff officer for Major General George B. McClellan in the Army of the Potomac's 1862 Peninsula Campaign.
Early in the Gettysburg Campaign, Custer's association with cavalry commander Maj. Gen. Alfred Pleasonton earned him a promotion from first lieutenant to brigadier general of volunteers at the age of 23.
Custer established a reputation as an aggressive cavalry brigade commander willing to take personal risks by leading his Michigan Brigade into battle, such as the mounted charges at Hunterstown and East Cavalry Field at the Battle of Gettysburg. In 1864, with the Cavalry Corps under the command of Maj. Gen. Philip Sheridan, Custer led his "Wolverines" through the Overland Campaign, including the Battle of Trevilian Station.
Custer, now commanding the 3rd Division, followed Sheridan to the Shenandoah Valley where they defeated the Confederate army of Lt. Gen. Jubal A. Early in the Valley Campaigns of 1864. In 1865, Custer played a key role in the Appomattox Campaign, with his division blocking General Robert E. Lee's retreat on its final day.
At the end of the Civil War (April 15, 1865), Custer was promoted to major general of volunteers, but was reduced to his permanent grade of captain in the regular army. In 1866, he was appointed to the regular army rank of lieutenant colonel, leading the 7th U.S. Cavalry and served in the Indian Wars. His distinguished war record, which started with riding dispatches for Winfield Scott, has been overshadowed in history by his role and fate in the Indian Wars.
Custer was defeated and killed at the Battle of the Little Bighorn in 1876, against a coalition of Native American tribes composed almost exclusively of Sioux, Cheyenne, and Arapaho warriors, and led by the Sioux warrior Crazy Horse and the Sioux leaders Gall and Sitting Bull. This confrontation has come to be popularly known in American history as Custer's Last Stand.