US forces fought at Cantigny on May 28th, 1918, and Chateau Thierry five days later, but they were only skirmishes. Belleau Wood (June 1-26, 1918) is generally accepted as the first major US battle of World War 1, and the first major US battle in a foreign war since the 1840's. General Pershing referred to it thus; "the Battle of Belleau Wood was for the U.S. the biggest battle since Appomattox and the most considerable engagement American troops had ever had with a foreign enemy".
It is certainly the best remembered US battle of WW1.