I have been searching online trying to find specifics for when the systematic killing of the Jews took place but there seems to be a lot of uncertainty. I was just wondering if the propaganda film was released as the Final Solution had begun.
Christopher Browning notes in Ordinary Men that
In mid-March 1942 some 75 to 80 percent of all victims of the Holocaust were still alive, while 20 to 25 percent had perished. A mere eleven months later, in mid-February 1943, the percent ages were exactly the reverse. At the core of the Holocaust was a short, intense wave of mass murder.
Similarly, Saul Friedlander entitles his book spanning the years 1939-1945 The Years of Extermination in contrast to his previous book The Years of Persecution and makes continual mention of Hitler's 1939 prophecy (that if the Jews "caused" another World War they would be exterminated). Even by March 41, he discusses a "forthcoming 'war of extermination'".
All of that seems to suggest the Holocaust came about significantly later than Triumph of the Will. Clearly the film's purpose was to promote the recent Hitler dictatorship (Hitler became Fuehrer only in 1934), but if by the Holocaust we mean an era of mass killing, then no Triumph of the Will did not come out at the same time.
EDIT: To clarify, Hitler became Chancellor in 1933. Shortly thereafter the Enabling Acts were passed, concentrating vast powers into Hitler's hands. Hindenburg died in 1934 and it is with that the office of the presidency was completely abolished and Hitler declared himself Fuehrer.