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.
Scale for sure. Not just in terms of how far they were able to travel, but how big everything is and how many resources they would take to build, not to mention time.
Even if we knew exactly how to build everything in the movie, it would still take a TON of time to build it. Now start in the future and work backwards -- it's simply unrealistic.
That isn't to say that we won't have tons of things even 100 years from now that we can't imagine currently. I just tend to think the unimaginable is more easily attained than the evolution of those things already made.
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.