Is there a single English word that describes the geographic place and time of a person's birth?
My real question is how do I express where I was born at a particular time in history with a single word.
I doubt there is any such word. Natal time and Natal place are two different elements and not often combined. Only horoscopes use both that I know of, and if they have one term it might well be considered jargon.
No. They are two different concepts and cannot be described with a single word. The shortest can be
I was born on 12/12/1800 in Oxford.
Setting seems to be a general term used to specify both time and place, but not specifically for birth.
Following on from earlier contributions, I suggest 'natality.'
In English, following an olde tradition we use an ISO 8601 timestamp with a UTC timezone offset. That indicates the time and date, and narrows your birthplace down to one timezone, which is good enough for most uses. This also has the advantage of reducing North-South discrimination.
Origin. My origin was Germany on such-and-such a date. It does tend to strongly suggest a location, more than it does time. For time, it may need a little help (like the word "on", as shown, or "at"), but if you mention a time, people will understand you mean your birth time because of the word "origin".