The museum, Mr. Bunch said, captures a symbolically important moment at the end of the Obama presidency, and he is relieved that its completion comes before the president leaves office.

But the Obama story commands relatively little space — one display case and part of another focusing on 2000 to 2015. There will be, among other things, a clip of his 2008 speech on race in Philadelphia and the text of his 2013 speech at the 50th anniversary of the March on Washington.

Mr. Bunch said he would leave it to the Obama presidential library, planned for Chicago, to give the president greater focus.

And the Obama presidency is decidedly not the end of the story the museum means to tell. A Justice 4 Trayvon placard and a Black Lives Matter T-shirt underscore the issues of persistent inequality and police brutality. “Building the story of African-American history to me feels important, timely and perhaps more timely than I hoped it would be,” said David J. Skorton, secretary of the Smithsonian Institution.

Following the death of Mr. Gray in Baltimore last year, the curators collected artifacts and recorded videos that may be displayed in years to come. The final experience that visitors will have along the historical timeline will be watching taped interviews about identity, activism and race with five people, including Opal Tometi, a Black Lives Matter organizer, and Jay Smooth, the disc jockey and commentator.

“We wanted to make sure that people didn’t see the first African-American president as the end of history for African-Americans,” said Michelle Joan Wilkinson, one of the curators. “Very soon after people walk into this museum, Obama will not be president. So what are the questions that we need to continue engaging with beyond a black president? We all agreed with that. We had to figure out how to do it.”