wrote:
I'm curious. Suppose I were to be deprived of technology and had to
rely only upon my observation, and intuition, how would I know that
Earth's axis is inclined at an angle instead of being perpendicular?

How did the ancients know that the axis of Earth is not perpendicular,
but inclined ?

Sun, Moon, and stars wobble. Lots of ancient constructions are built to
mark the extremes of the wobble.