How is it possible that the ancient people knew that the earth is round?
There is no answer.

Yes, there is an answer. If you measure the angle of the sunshine when the sun is at its highest point in the sky in two locations on the same day, you can calculate the Earth's curvature.

Eratosthenes did this in Alexandria around 250 BCE. He calculated 40,320 km. He was only in error by 290 km or ~0.7%. The learned have long understood that our planet is spheroidal.

Having said that, I agree that both astika and nastika Dharmic texts have displayed incredibly advanced scientific and spiritual understanding.