Military brass bands were used to boost morale at home, in camp, and on the battlefield. They used famous bands joining certain regiments to get recruits to enlist. Some bands had 68 pieces and were under contract. The band wore colorful, elaborate costumes and it was easy to spot them apart from the soldiers in uniform. Some bands were made up of just talented soldiers.
Boxing, broad jumping, wrestling matches, foot races, hurdling, mock fighting all took place in camps during the civil war as a past time.
There were louse races: basically soldiers picked lice off each other's head and raced them. So there's that.
1860's saw the founding of the semi-pro national baseball clubs.
Baseball was founded in groups of men that had homemade equipment and has loosely interpreted rules they often made up themselves.