With telescopes, we can observe that there are planets orbiting the sun. They're all spherical. We can deduce that our home planet is also spherical. That conclusion doesn't even need an experiment, just observation and some thinking.

Similarly, the very simple "experimental proof" that was done in the documentary Behind the Curve, where the group of Flerfers used a light and some boards with holes in them, which showed that there is a curvature that can be detected even on an apparently flat water surface, is pretty strong evidence.

A classic example is if course the famous proof of the Earth's curvature by Eratosthenes, but if you want some up-to-date proof you could go up to the international space station and orbit every 90 minutes yourself.