I googled a little. It is barely possible under ideal conditions to discern the curvature of the earth from an airliner at 37,000 feet. You need a 60 degree filed of view and a cloudless horizon, and you're just barely going to see it.
Now it's easily visible from the International Space Station, but our hero would probably say that thing is fake.
But anybody can go to the ocean and watch objects drop below or rise up from the horizon there, a phenomena only explainable by a round earth.
see
https://earthscience.stackexchange.c...ble-to-the-eye