Non flat earther here and I would like to propose an argument.

Explain how the Ancient Greeks viewed the Earth itself as a globe?

"By the 5th century B.C., it was widely accepted that the Earth is a sphere. This is a critical point, as there is a widespread misconception that ancient peoples thought the Earth was flat. This was simply not the case.

In the 5th century B.C., Empedocles and Anaxagoras offered arguments for the spherical nature of the Earth. During a lunar eclipse, when the Earth is between the sun and the moon, they identified the shadow of the Earth on the moon. As the shadow moves across the moon it is clearly round. This would suggest that the Earth is a sphere."