It's impossible to say definitively which distance from Earth was measured *first* as early civilizations had different understandings of the universe and methods of measurement. However, we can talk about some of the earliest attempts to measure distances:

* The distance to the Moon: The ancient Greeks, particularly Aristarchus of Samos, attempted to calculate the distance to the Moon using geometric methods based on lunar eclipses. While their estimates were not accurate by modern standards, these attempts mark an early understanding of the relative distances in the solar system.

* The distance to the Sun: Eratosthenes of Cyrene, around 240 BC, famously calculated the circumference of the Earth with surprising accuracy. However, the distance to the Sun wasn't measured accurately until much later, with advancements in astronomy and the development of more sophisticated instruments.

* The distance to nearby stars: It wasn't until the 19th century that astronomers were able to accurately measure the distance to stars using the method of parallax. This technique involves observing the apparent shift in a star's position against the background of more distant stars as the Earth orbits the Sun.

Therefore, while we can pinpoint early attempts to measure distances in the solar system, determining which distance was measured "first" is difficult due to varying definitions of measurement and the limitations of early methods.