I watched 'Beyond the Curve' and the comments about some people desperately seeking evidence that supports their own unscientific theories, and the Dunning- Krueger effect displayed by flat-earthers, led me to look into some historical investigations which I present here as a simple story.
The Greeks worked out 2500 years ago that the earth is a sphere, because they looked up. In the day there was a round sun and at night there was a 'round' moon that looked 3D, and very occasionally the shadow of the earth showed as an outline on the moon. Simple deduction told them that the earth was a sphere like the sun and moon, but we had to wait until Galileo and his telescope 2000 years later to work out we were not at the centre. This is the '500 years' that flat-earthers often quote in their deranged conspiracy rants, but inconvenient facts don't change closed minds.
2250 years ago, a Greek called Eratosthenes looked down a well in southern Egypt at mid-day on the summer solstice, and saw the sun reflected in the water below, so he sussed that the sun was directly overhead. Next midsummer he was in Alexandria, so he plonked a stick vertically on the ground and measured the length of its shadow. Knowing the length of the stick, he was able to work out the angle of the sun at about 7.2 degrees, or about one 50th of a circle. He had paid attention in geometry class! Erato knew it was about 500 miles from the well at Aswan to Alexandria, so he calculated 50x500 = 25,000 miles which turned out to be a pretty accurate stab it the circumference of the world.
There were some clever buggers around all that time ago. We have known this stuff for over two millennia, which is a long time to keep a conspiracy going!