[TillE]

If you understand the basics of physics and the nature of Earth and the moon, as we did by about 1700, it's easy enough to grasp how you might get from one to the other given sufficient energy. A little over 250 years later, it happened.

I wouldn't necessarily rule out a major breakthrough in space travel, though it seems extremely unlikely. But transporter technology is so wildly implausible as to be effectively impossible, certainly in that time frame. Reassembling a full human being doesn't even begin to fit our current understanding or any suggested theory of physics.