They were outvoted or simply not listened to, you mean.
Otherwise, the argument becomes circular: "Clearly there was no significant possibility that the Japanese Cabinet would have agreed to surrender had not the first two bombs been dropped. As evidenced by the fact that the bombs were dropped, and they did, after all, surrender."
It's more like "As evidenced by the fact that even after the first was dropped they were not willing to surrender, and after the second was dropped the Supreme War Direction Council or Inner Cabinet was still deadlocked on what to do."
Two atomic bombs being dropped on them was not decisive in getting the Cabinet to decide to surrender. It took the Emperor's involvement to break the deadlock and even then there was a coup attempt to stop the surrender:
What action(s) with less weight/influence than two atomic bombs and the Emperor could have swayed the Japanese Cabinet? And even those things were only barely over the line:
> When word of the emperor’s decision reached General Toroshiro Kawabe, the Vice Chief of Staff of the Imperial Army, he noted in his diary that he concurred with another senior general in doubting that the overseas commanders would comply with the emperor’s order. That these officers correctly doubted even an order from the emperor would secure compliance with key parts of the armed forces, was swiftly confirmed by messages from the commanders in China and the Southern Area, declaring they would not comply with the surrender. Their commands mustered between a quarter and a third of all Japanese servicemen. It took Hirohito’s personal emissaries to persuade these commands to surrender.
