IT begins with an emotional wallop that is especially powerful because it is delivered offhandedly. The first minute of the six-hour, three-part documentary series “The US and the Holocaust” features a black-and-white photo of Otto Frank, who had been a German officer in World War 1, strolling in Frankfurt, Germany, with his wife and two daughters. It is March 1933, and Adolf Hitler has been chancellor for less than two months. One of the daughters, Annelies, the world now knows as Anne. She would write a diary even though she doubted that anyone would ever be interested in “the musings of a thirteen-year-old schoolgirl.” She was mistaken.

In early 1934, the Frank family would be living in Amsterdam, hoping, like many Jews from Germany, to reach the United States. The Franks’ hopes, and those of most others similarly situated on the edge of Europe’s abyss, would be crushed.

The Ken Burns, Lynn Novick and Sarah Botstein documentary, which premieres Sunday on PBS, rekindles an agonizing debate: What and when did the US government know about Nazi genocide, and what could, and should, it have done better? The answers that the film judiciously suggests lack comforting clarity.

As the documentary notes, the United States admitted about 225,000 refugees from Nazi terror, more than any other sovereign nation — fewer than it should have but more than public opinion favored. Before Hitler attained power, America’s receptivity to immigrants had waned, and anti-semitism, especially in society’s upper reaches, had not. Today’s white-nationalist anxieties about “replacement” recast the anxiety of the prominent eugenicist Madison Grant: “The man of the old stock is being crowded out.”

In the 1920s, Henry Ford’s antisemitic newspaper had the nation’s second-largest circulation, according to the documentary. “In 1932,” it reports, “for the first time in American history, more people left the United States than were allowed in.” In the mid-1930s, more than 25 percent of the population listened each Sunday to Charles Coughlin, an anti-semitic radio priest.

US newspapers published abundant reports of German anti-semitic lawlessness, but many readers were skeptical, remembering discredited World War 1 propaganda about German atrocities. The State Department, hospitable to upper-crust anti-semitism (the documentary names culprits), made visas difficult for German Jews to acquire, then cited the few applicants as evidence that Germany’s Jews were not in crisis. America’s millions of moviegoers saw newsreels in which content about Germany was usually produced by Hitler’s government.

Because Congress would not liberalize immigration, President Franklin D. Roosevelt could not ask other nations to do so. He did say that all Jews who were in America as tourists could stay. But when the United States entered the war, fear spread that European immigrants might include Axis agents. The chairman of the Senate military affairs committee favored building a wall around the nation “so high and so secure” that no alien or refugee could enter.

Three-quarters of the Holocaust’s victims were murdered in 20 months, deep in Eastern Europe, before there was a US soldier on the European continent. The victims could not believe what was happening to them; neither could distant Americans. When, at last, in 1943, the reality of industrialized murder became known, the pace of killing slowed because there were too few readily available Jews to be delivered to the death machinery.

By 1944, with 5 million Jews already dead, 70 percent of Americans now favored sheltering European refugees, temporarily. US officials were neither wrong nor reprehensible when they argued that the best way to help the Jews was to win the war as quickly as possible. Bombing the killing camps would have diverted bombers from military targets, and — “precision bombing” was then an oxymoron — would have killed many Jews.

Some indecent attitudes, and then the inability of decent people to believe the reality of unbelievable indecency, prevented America from doing more than it did with its heroic World War 2 exertions and sacrifices. “The US and the Holocaust” is an immersion in the limitations that accompany, and define, tragedy.

A Holocaust survivor who speaks in the film, Eva Schloss, was a new refugee in Amsterdam when she became friends with another 10-year-old girl who had been in the city six years and was living in what was now their shared apartment block: “She introduced herself and said her name is ‘Anna Frank’.”

A photograph of her then, about five years before her death, radiates cheerfulness. It is an imperishable, unforgettable image of what can be lost when we forget how perishable is the thin crust of civilization that protects us — until it doesn’t.