National Museum of the American Indian, 2004, by Lautman, Robert, 2004, Smithsonian Archives - History Div, The National Museum of the American Indian opened on September 21, 2004. The museum was the first dedicated to American Indian culture and heritage on the National Mall. The building, designed by architect Douglas Cardinal, is five stories, with 250,000 square feet, and is located between the National Air and Space Museum and the U.S. Capitol..