At the time, the United States was the first and only country to have access to nuclear weapons thanks to research done in Project Manhattan. The US surrounded the Japanese islands and had the option of an all-out invasion of Japan, or drop the atomic bombs. The Japanese have a fierce military history and culture of fighting with death being a more desirable option than surrender which brings dishonor to those soldiers defeated. Honorary suicide, kamikaze, killing oneself in the face of adversity were highly documented Japanese incidents throughout WWII that proved the Japanese do not mind losing high casualties in the face of defeat. An invasion of the Japanese islands would involve millions of Japanese and American casualties, as Japan being an archipelago would involve several different amphibious invasions that would see a greater destruction over the country with more cities and land being destroyed in comparison to two bombs being dropped on two cities. For these reasons, the atomic bomb dropping was justifiable at the time as it lead to fewer deaths in comparison to an invasion that would be more costly and time consuming.
