As far as I can tell, there are two possible scenarios:
Scenario 1. The earth is round, despite appearing flat to the casual observer because of its enormous size. The Greeks proved this like 2000 years ago. Since then, lots of folks have made observations and done experiments to further understand the size, structure, and motion of the earth, sun, other stars and planets, galaxies, etc. People have also developed technology which has allowed them to do some pretty amazing stuff, like propel large objects beyond earth's atmosphere, and survive in the vacuum of space. They've also built submarines which can safely carry people to the bottom of the ocean, and airplanes which transport millions of people per day, through an environment that would otherwise be completely inhospitable.
Scenario 2. The earth is flat, yet some mysterious group has engaged in a coordinated disinformation campaign lasting for centuries, to convince the majority of people that it is round. People are indoctrinated into this way of thinking basically from birth, and are constantly exposed to new "scientific discoveries" to further elaborate and expand on the hoax of a round earth floating in space. Thousands of "them" have worked on the campaign, creating everything from fake pictures and videos requiring extensive set and prop design, to giant telescopes and other "scientific instruments" such as the Very Large Array and LIGO, which either serve no purpose other than perpetuating the hoax, or have some nefarious purpose known only to "them." Any experiments which might provide legitimate evidence that the earth is flat are quickly discovered by "them," and either discredited or silenced before they can be released to the masses. The end goals of the campaign are sort of unclear, and so far, no one involved in it has ever been able to come clean to the public, at least not in a way that gained much traction or credibility. Because of the breadth and depth of the disinformation campaign, very little is known about the true structure of the earth and its surroundings, except by "them."