For most of the last 75 years, it would have been impossible for a family touring Washington, D.C., to recreate the iconic photo of John F. Kennedy Jr. as a toddler, playing under the Resolute Desk in the Oval Office while his father directs the affairs of government.

That changed last week, when the White House Historical Association opened a museum and educational center across the street from 1600 Pennsylvania Avenue. At the center of the new, three-story facility is a full-scale replica of the office, complete with a duplicate of the famous desk that toddlers are welcome to crawl under.

“You can sit at the chairs in front of the fireplace like a president and head of state,” Stewart D. McLaurin, the president of the association, said during a recent pre-opening tour. “You can be, in your mind, a president of the United States, and the real president is just 150 yards away from where we are. You could pick up the phone, and you could either solve or start a world crisis.”

The museum has opened at a tumultuous moment, when the current president is dealing with several crises and a deeply divided nation is poised to choose its next leader. There are few, if any, references to current events, but Mr. McLaurin said the goal of the association was to provide visitors insight into the difficult choices that presidents face.