In the above scenario there is nothing that could prove the earth is a ball. Very strange and futile question.
Very good observation Simon. It's not supposed to.
The question is actually quite simple. Most flat earthers should be able to answer it without any problem. You claim the earth is flat because you don't see any curvature, right? The question is, what would you expect to see on this large Earth such that you would say "Hey, now I'm convinced teh Earth is a sphere!"
The thing is, even if the Earth was a sphere 12,742,000 meters in diameter, you still could not see a curvature. Given that, why do you think the Earth is flat? What is it you are seeing that you should not see on a spherical Earth 12,742,000 meters in diameter? If you are confused about the whole meters thing, use 41,804,460 feet. Would you expect to see a curve standing, or boating, on a sphere 41,804,460 feet in diameter?