First, its very important to remember that city bombings, AMD the targeting of civilins, wasn't new to then atomic bombings. Hamburg, Dresden, Tokyo, and a dozen more cities had been intentionally devastated by airpower using conventional bombs. Either of the two atomic bombs killed less people and destroyed less city than the massive conventional bombings did.
Second, while they're are some treaties which might suggest that atoimic bombing is unethical, they were promulgated after 1945. To put it another way, you cant charge a person for a crime which doesnt yet exist. Nor can you try them ex post facto after the act is prohibited.
Thirdly, the United States has never subscribed to those treaty provisions which prohibit the use of atomic weapons. Its not a crime here, because the IS government believes that there is a time (especially in the context of the cold war) when atomic strikes mihlght be necissary. To that end, battlefield commanders ad to be confident that they could do what it took to protect American allies, without potentially getting drug to The Hauge for doing so.
Typed on my mobile
I'm not sure if you mean Truman who authorized the use of the bomb or the crew of the "Enola Gay" somebody between the two or all of the above.
For Truman, he was the popular leader of a victorious superpower along with Churchill and Stalin. As the victors they got to assign blame and determine who would be tried for the crimes committed during WWII. Of the three Churchill, Stalin and Truman I would even argue that Truman committed the fewest crimes but as an American I may be a little biased.
For the intermediate generals and officers who planned and organized the dropping of the atomic bombs they could claim they were just following orders. Or they could claim they were saving lives by attempting to bring the war to a rapid close. Or they could argue that they thought the atomic bomb was more humane than the firebombing which was already devastating Japanese cities.
For the crew of the "Enola Gay" following orders would probably be a sufficient claim. The weapon they dropped was much more powerful but the action was very much the same as the bombing done by thousands of other bombing crews on all sides throughout the war.
With all of these I reiterate the single biggest factor is that the victors of a war don't go on trial for the crimes of the war.
This issue has been hashed over many many times. At the end of the day there is no consensus on whether the dropping of the atomic bombs is a war crime. The opinion seems to sway back and forth with the United States of America's popularity with the world. When people like the US they attribute the bombing to a necessary action to end the war. When people don't like the US it was a horrific massacre of innocent civilians done to demonstrate the power of the US to the Soviet Union and Japan. As with most political topics that are so polarized my position is that the truth is probably somewhere in the middle.
Some previous posts have great answers to help you understand all positions:
How have non-Americans typically viewed the usage of the atomic bomb during WWII?
The phrasing of your question assumes the action was a crime against humanity. It was certainly a horrific use of a powerful weapon but there are valid arguments that it was simply part of war. For politically charged topics like this I recommend you post the question with a more neutral tone to encourage discussion from people with varying viewpoints. If the phrasing is due to English not being your native tongue please do not misunderstand my suggestions to indicate that your post was undesirable.