It cannot be proven so.
It doesn't have to be. Science is not a metric for truth. Science is a metric for knowledge. Saying that "Science cannot prove the world is round" is absurd, because it is not the premise of (real) science to prove anything (the curvature of the world or otherwise). You seem to have taken this to mean that I am trying to prove that the earth is flat.
No. I'm saying you're stating a false hypothesis, which has been positively falsified on several occasions, independently of one another. Not because it was the most convenient hypothesis, but because it was false. A more suitable statement would be science cannot (yet) prove that the Earth isn't a hypersphere (or rather is not round, in the traditional sense), because science can most definitely and irrefutably prove that the Earth isn't flat. Its not, its based on self supporting Hypothesis
A self-supporting hypothesis is not science either. In order for a hypothesis to be considered science, it must at the very least, be potentially falsifiable, and supported by empirical observations and experiments. For the better part of 2000 years (from Aristotle to Newton) it was believed that an object weighing ten times as much as another object, would fall to the ground ten times as fast when dropped. Why? Because in almost 2000 years, nobody thought to do an experiment to see whether the hypothesis was accurate.