What is the antonym of terminal?

Terminal is not commonly used in the sense you describe. If you buy a ticket from point A to point B, point A is your origin and point B is your destination.

On a fixed route such as a railroad, each end of the line is known as the terminus; while this word refers to a final end point, which point is the start and which is the end obviously depends on your direction of travel. Terminal, on the other hand, usually refers to the building or other facilities where travel begins and ends.

I'd use origin. "Place of origin," like "place of departure" would obviously be more specific, but for a single-word antonym, that should serve.

I too would find origin confusing in this context. "What is/was your origin?" could mean many things, such as your ethnic origin, place of birth, etc.. The meaning "Where did you start your journey?" would not be a meaning that would normally occur to me on hearing "What is/was your origin?".

Personally, I would use starting point, departure point, or something similar.