The prevailing sentiment was that the Japanese would not surrender until their home islands were totally conquered. Their government was in the process of preparing the civilian population to fight to the death. (Research the invasion of Okinawa if you want to know what a US invasion of the main island would have been like.) In a version of the trolley dilemma, the American rational was that the loss of life in two horrific attacks that would shock the Japanese into surrender was less evil than the alternative of invading their home islands.

I'm not making that argument, or saying there were no alternatives, just that the Americans were weighing the loss of life (including civilians) involved in a nuclear bombing against the loss of life (including civilians) in invading the islands.

Notwithstanding other unthought of solutions, the strategy worked, and the apparent alternative would have been brutal.