When and how was it discovered that the sun was in different positions depending upon longitude?

It seems to me that the ancient Greeks knew that geographic location affected the apparent position of the sun in sky but given the lack of rapid travel or communications or reliable clocks, how was this ever discovered?

I am guessing that travelers might have noticed that their own internal clocks became out of synch with the local time but again, travel was so slow that I assume there really was no "jet lag" — moving at most, aboard a ship which I think would have been the fastest was to move large distances, about 100 miles a day the change in local time from that of the traveler’s origin would have been too slow for any jet lag-like phenomenon.

EDIT: I understand that once it had been concluded that the Earth was round and revolved, an unusually educated person would understand, perhaps, that this implied that the sun would be in a different position in the sky at the same time to people in two far-apart cities.

But I would suggest that very few people could visualize this idea. There was no way to communicate to the person in the distant city — the idea of simultaneity might have been very hard to grasp, again, since time and solar position were so tightly coupled.

There was a very clever (I assert) inventor who devised a time-keeper for court in ancient Greece and he made provisions for the time-keeper to run differently at different times of the year — he did not have, I think, the idea of an hour but rather some equal division of daylight. Abstract time may not have been a thing to the ancients and therefore simultaneity in two distant locations may not have been a thing.