Here's an interesting old silent film from the Spanish-American War. It was filmed in 1898 by Edison Studios and shows the steamer Mascotte docked at Port Tampa, Florida, on its way to Cuba. The 2d Battalion of Colored Infantry is going ashore. The tide is very high, and the gang plank is extra steep, so the soldiers have to be careful coming down. Their commanding officer is on the wharf trying to get them to hurry.
Black troops played a prominent role in the capture of Cuba from the Spanish and participated in most of the major battles, including the famous charge up San Juan Hill. The African-American press was divided over the war, some editorials saying that black troops shouldn't fight abroad until they gained equality at home, while others said that it was a patriotic duty and would lead to more respect for the black community. The debate continues to this day.
I believe this is the first film of black troops in the U.S. army. Given the date, it certainly must be one of the first.