We typically say that there were two different “official” beginnings because there were two somewhat separate parts of the war.
In Europe, we say that the war officially began when Germany invaded Poland. This happened in September of 1939. This was the official beginning of the war because it was the first time that any country actually stood up to Germany and declared war on it. Germany had previously taken Austria and Czechoslovakia without serious fighting. France and England said they would declare war on Germany if it attacked Poland. When Hitler called their bluff, they declared war, thus beginning what came to be called World War II.
In the Pacific, the war officially began when the Japanese attacked Pearl Harbor on December 7, 1941. Japan had already been fighting against China, but that is not typically considered to be part of WWII. The Japanese felt that they needed to prevent the US from interfering as they took an empire for themselves in East Asia. Therefore, they attacked Pearl Harbor. This started the war in the Pacific.