Did World War 2 first start using atomic bombs?

No, it started formally when Hitler ordered a faked Polish attack (by German soldiers wearing Polish uniforms) on a German radio station on September 1, 1939 (although fighting had been going on for several years before that between Italy & Ethiopia and Japan & China). In "retaliation" for this faked attack, Hitler declared war on Poland and invaded.

The war was ended by the first use of atomic bombs ever in combat when two bombs were dropped on Japanese cities: Hiroshima on August 6, 1945 & Nagasaki on August 9, 1945.