We have measured the distance of the Moon from the earth using various methods, including lasers. One can shine a bright laser at the moon and have the light reflected back. Using the speed of the laser and the reflected light, we can figure the distance the light traveled.
That would be roughly 239,000 miles. Since the moon appears between the earth and the sun, the sun is not 3,000 miles from the earth, according to the distance of the moon from the earth.
The sun would need to be much further than 239,000 miles.
The ancient Greeks also figured this out using more primitive means, and their tests can be done using two people with long-range communications (cell phone). The distance derived from these tests supports the laser tests of the moon's distance from the earth.