I think you have your chronology a little confused.
Concentration Camps began right in 1933, first in the phase of the "wild camps" set up by all the various Brownshirt groups in various towns, often comprised of single houses or prison facilities; the first larger one was Dachau (in Munich); then, in 1936, for the Olympic Games in Berlin, the Nazi regime needed a PR-clampdown for better international press coverage, and shut down the many political prisons in Berlin particular which would have "looked bad" to the many international visitors in town, and replaced it with a more "official" large scale concentration camp, which opened in the spring of 1936 north of Berlin (the infamous Sachsenhausen camp in Oranienburg, north of Berlin), about twenty miles outside of Berlin. To Sachsenhausen, the Nazi regime invited visiting delegations of the International Red Cross to "show that they had nothing to hide" and that "concentration camps were just regular prisons." (Which of course they weren't, because during the delegation visits the camps put on a "show", moving all prisoners with bruises etc out of sight). While the red cross delegations were duped and could not get a majority vote together to officially condemn the practice of these political prisons, the public knew better what they were (there were plenty of whispered German jokes at the time about concentration camps betraying a general understanding of what was going on inside). At this point, however, Jews were not yet brought to camps as a rule. While many inmates were Jewish at this point, they had at this point been brought there for other charges (being member of a labor organisation, communist, social democrat, "work shy", other trumped up charges, or simply being a member of any other disliked political groups or organizations by the regime).
Camps at this point were not yet the death camps of the genocidal machinery that began its work in 1940/41. So, while there were not yet gas chambers in any of the camps at this point, since the Nazi Nuremberg Racial laws of 1935 it was quite clear that the regime had on its mind the utter isolation and expulsion of Germany's Jews. German government policy switched to one of destruction of all European Jewry and other declared enemies of the Nazi state only later, but camps already existed, and Jews were already treated horribly in many ways when Chaplin sat down to write his famous movie script through the second half of '38 into 1939.
At this point, German Jews had been declared non-citizens, tens of thousands had fled the country, the synagogues had been burnt in the so-called Kristallnacht, which is more aptly called the pogrom night, Austria had been annexed, another big concentration camp had opened there right away (Mauthausen), and as filming of The Great Dictator began in September, Germany invaded Poland.
In short, Chaplin had seen and heard plenty of evidence about the camps when he began filming. Asked after the war whether he could ever have made a comedy about the Nazis had he known what horrors were about to happen in the camps and elsewhere, he replied in the negative.