IMHO the first marine mission like we think of today was the one William Eaton led in the First Barbary War.
“From the Halls of Montezuma” : This refers to the Battle of Chapultepec in September 1847 during the Mexican-American War. Marines stormed Chapultepec Castle, a fortress on a hill in Mexico City that was once part of the Aztec capital, which ultimately led to the capture of the city.
“To the Shores of Tripoli” : This refers to the 1805 Battle of Derna, which was fought during the First Barbary War. Marines, led by First Lieutenant Presley O’Bannon, marched across the desert to capture the city of Derna and raise the American flag for the first time over a fortress in the Old World.