Technology and magic
Any sufficiently advanced technology is indistinguishable from magic. Any sufficiently advanced aircraft is indistinguishable from an alien ship!
Area 51 in Nevada, USA is widely depicted as the place where the US Government conducts experiments on extraterrestrial vehicles and aliens. Or even a place where they conduct meetings with extraterrestrials. How did Area 51 earn this bizzare reputation?
In the middle of the Cold War, the US was paranoid about the development of nuclear weapons by USSR. So there was a need to develop surveillance capabilities. The best possibility then was the development of an aircraft that flew so high in the sky that Russian missiles couldn't reach it, and one that flew so fast that Russia's aircraft couldn't catch up with it. The result was a series of aircrafts that were decades ahead of their time.
Lockheed created some of the iconic aircrafts like the U-2, the A-12, and the SR-71. All these aircrafts were tested around the Area 51 test site. These planes flew much higher than regular military aircrafts of the time. Where a regular military aircraft might fly at 40,000 feet, these aircrafts flew at 65,000 feet or even higher. They were also among the fastest planes ever built. The SR-71 achieved a top speed of 3.5 mach (i.e. 3.5 times the speed of sound). Even today, the fastest military aircrafts (apparently the MiG-25 Foxbat) flies at a leisurely 2.83 mach.
These planes were also incredibly secret. So even most armed forces personnel did not know about their existence. So when they would be flying their regular missions, they could often look up to see something shaped like a saucer or a bullet speeding along at super-human speeds. They were also mostly sighted late in the evening when their undersides caught and reflected light from the setting sun - making them look like a shimmer. Is it surprising that they thought these were alien spaceships?
Interestingly, these conspiracy theories actually became great cover stories and helped keep these aircrafts a secret for much longer than they otherwise might have.
The stories about these aircrafts and the teams that built them (notably, the Lockheed skunk works) are incredible and worth learning about. But it is also a testament to the power of intense rivalry and sense of urgency in prompting innovation. Is it possible to replicate the same sense of urgency without being in a "cold war"?