This page goes over the possibility of the US victory at Little Bighorn.. The defeat at little bighorn was largely because of the beef between Major Reno/Captain Benteen and Lt.Col Custer. Reno and Benteen were not loyal to custer, neither was it the other way around. However, a victory is not impossible.
Before the battle begins, Custer accepts the Gatling guns and the extra battalion. Although he can wait for Philip Sheridan, he decides to go for the victory and erect a defensive position and create a bait for the Indigenous Americans to attack the foritified positioons with Gatling Guns.