How about Eisenhower? I feel like this is fairly good evidence.

https://www.trumanlibrary.gov/education/lesson-plans/re-thinking-dropping-atomic-bombs-lesson-2

“During his recitation of the relevant facts, I had been conscious of a feeling of depression and so I voiced to him my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives. It was my belief that Japan was, at that very moment, seeking some way to surrender with a minimum loss of ’face’. The Secretary was deeply perturbed by my attitude…”

• General Dwight Eisenhower, 1963

What type of evidence are you looking for? Every firsthand account of people involved in the decision makes it clear that:

• they believed a land invasion would be brutal
• they believed Japan would not surrender easily
• they believed using nukes would force surrender faster due to unprecedented force
• they chose targets to maximize weapon effect on target measurements
• they chose targets and timing to maximize visibility to the Soviet Union
• they decided upfront that anything short of unconditional surrender was unacceptable
• they believed terror must be maximized because there were only two bombs

They’re perfectly capable of wanting to prevent an invasion and wanting data.

Most seem to agree that Japan had already lost before the nukes. Whether it would have been “better” than dropping the bombs and how long it would have taken is the bigger debate.

How far would Russia go once it turned its eyes on Japan? And once, or if, they began pushing the Japanese out of mainland Asia would that change US strategy?

How long would the Japanese populous endure famine and starvation before revolt? Would they even revolt?

Would the US do a land invasion after seeing how much, and how long, Iwo Jima and Okinawa took? Or just bomb and blockade?

Would any of the three even try and get the others to a table to negotiate some form of peace?

Who knows since it is all speculation.

The evidence is the positions of troops and assets of Japan and the US during that time. An invasion of the Japanese homeland was imminent.