It's been demonstrated to work. There's no way to get something from Vandenberg to Kwajalein Atoll ballistically without getting a minimum amount of launch speed. If you can attain that speed, just by pointing the rocket straight up you'll get a lot of altitude... high enough to see that the Earth is round.
As for the proof, there are plenty of photographs of the launches & landings. Of course, you could always claim that they aren't causally related, and the whole thing is made to fake the working of rocket technology.
Of course, the government was also "in" on the plot to blow up the barracks at Dhahran and sneak some missiles into the air over Saudi Arabia and make them
look like they were launched from Yemen! That's why they were intercepted!
And the V-2 most definitely was FAKE NEWS. The UK had absolutely
nothing to worry about. They were in collusion with the Germans to convince everyone that rockets actually worked (even though they didn't have any...).
Let's not forget the Iran-Iraq war. Wow! Two mortal enemies collaborating to help the USA maintain that its rocket technology works!
And then NASA...
The purpose of NASA is to fake the concept of space travel to further America's militaristic dominance of space. That was the purpose of NASA's creation from the very start: To put ICBMs and other weapons into space (or at least appear to). The motto "Scientific exploration of new frontiers for all mankind" was nothing more than a front.
Even if their ICBMs didn't work, they still were concerned about making them look like they worked? Please remind me why again?
I know the resolution to all of these problems! There is a dome above the Earth that stops all the rockets...