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.