People all across the world have known of the idea of using geodetic coordinates to describe location for a very long time. The ancient Greeks, Indians and Chinese knew that the earth rotated around its axis, and many of them, in particular Eratosthenes from Greek and Aryabhata from India made very precise calculations of the size of the earth and period of rotation. From these, you can theoretically calculate latitude and longitude. And in the middle ages, the Arab mathematician al Biruni offered detailed trigonometric formulas for calculating geodetic distances.

However, in practice the determination of longitude requires a concept of universal time, which is hard to measure. Local time is easy, but in order to coordinate the time between two different locations, you need to physically carry a clock between them. This was impractical since clocks relied on stability to keep time, and a moving clock quickly became inaccurate.

So while many astronomers in different parts of the ancient world could use math to calculate the difference in physical location between two places (which amounts to latitude calculations, whether you call them that or not), they could not do it on a moving vehicle such as a ship.

There have been many ideas for calculating a universal time astronomically (meaning, from the observation of some astronomical configuration alone, without needing to know your local time). For example, observations of conjunctions of the moon and planets, closest approaches (appulses) of various sky objects, eclipses, etc. But none of these was very precise, given the nature of instruments available at the time, and all failed pretty miserably when used on board a pitching ship.

Note that you can in fact measure latitude at various spots along your journey. Ships used this by "westing" or "easting", which was the practice of finding a latitude along which you expected to find your target, then moving exactly east or west along it until you hit land. The land might be an island on the way, in which case you could get off and take precise measurements on land. But this meant going far out of your way, because you were not taking a great-circle route to your destination.

So the actual measurement of longitude while in voyage had to wait for the development of a chronometer that worked aboard a ship, which as you know, was invented by John Harrison in the 18th century. He initially used counter-weighted beams with his first chronometer in 1735, but realistically, his first chronometer that was sufficiently precise was H4, with the invention of the balance wheel in 1760's, for which he won the longitude prize.

So, to answer your question, astronomers across the world in many different cultures have known of the concept of geodesic coordinates, and have worked out the math to use them, and even used them on a limited scale on land. But the determination of longitude on a ship is relatively very recent, and happened first in England.