I am sure it was all done but the paperwork when FDR passed on.
Roosevelt died April 12, 1945.
The first atomic bomb was exploded at Trinity, NM on July 16, 1945.
Harry Truman, the VP, wasn’t told of the Manhattan Project until after FDR’s death.
Trinity (first a-bomb exploded) - July 16, 1945.
Hiroshima - August 6, 1945.
For a fellow who didn’t even know of the atomic bomb before he became president, Truman didn’t let any grass grow under his feet before he used it.
And the mood in the country at that time was such that most Americans heartily approved.