They are US Army. The Marines of that time worn a different uniform and cover (hat).
I enlarged the insignia and it is not Infantry, but the crossed cannons for the Artillery. The rifles are not 1903 Springfield, but Springfield Model 1982-99.
“The Springfield Model 1892-99 Krag-Jørgensen rifle is a Norwegian-design bolt action rifle that was adopted in 1892 as the standard United States Army military longarm, chambered in U.S. caliber .30-40 Krag. All versions and variants were manufactured under license by the Springfield Armory between 1892 and 1903. The U.S. Krag was replaced beginning in 1903 with the introduction of the M1903 Springfield rifle. - The Blue Wool Army Uniform Coat was worn Post Civil War through 1898. Until the Spanish American War the US Army blue wool uniform was the issue for all seasons. As part of the redesign effort spawned by our military campaigns in tropical areas a complete redesign effort was mounted. Although the traditional army blue uniform was slated to be slowly phased out, they were still in issue in many areas through 1910. The legacy of Army Blue lives on, in the current day dress uniform worn by officers and enlisted.
Five bright raised shield US eagle buttons were used to close the coat.. It had a rolled falling open collar. and no external pockets. The jacket had a standard cuff fixed with three small bright eagle buttons that had no purpose other than decorative. It also had a and a band of stitching nearly three inches above the cuff. The jacket was fully lined with a black cotton liner and included a single interior breast pocket. There were no shoulder tabs and seams were single sewn. The jacket was constructed of blue wool and most surviving specimens seem to be of a standard color. “