The main point is that you cannot prove the globe model. With tools on this earth, without referring to things beyond the literal border of our experience. This means that you cannot 'invent' a system of rules with which to prove that what we cannot touch or measure with physical tools.
That means that you cannot use things like triangulation with the sun, or stars, to calculate a distance on earth, as we do not KNOW the distance to the stars, sun and moon. This assuming that we did not go to the moon.
The user experience is that almost everyone on earth has never seen the curve of the earth. All we see is a flat horizon.