I saw a video (that I can't currently find) of Feynman explaining this once.
The US government had a classified program that suspended 1940s saucer microphones from a balloon at a height in the atmosphere that would allow them to listen for Soviet atomic tests.
The balloon crashes and some reporters are out sniffing around. Someone with loose lips lets slip that it was a flying saucer. You can imagine what the artist's rendition based on that description looked like.
Then, since the program was classified, the official explanation becomes that it was a weather balloon or something, and a conspiracy theory is born.
It was most likely first used after Kenneth Arnold's famous report where he described a "saucer-like" shape. That story blew up, and people started reporting "flying saucers" everywhere.
It even got into the heads of some government officials. For example, the initial press release given by the airforce for the Roswell incident was that they had captured a "flying disc". They later made a correction that it was a weather balloon, but you can see how the government making such statements would cause confusion and add to the mania.
On the Wikipedia page for the incident you can see the original news articles: https://en.wikipedia.org/wiki/Roswell_UFO_incident
https://www.theatlantic.com/technology/archive/2014/06/the-m...
It’s quite possible that what he saw was the YB-35 or a similar experimental aircraft.
In 1947 your cockpit would likely not even have a true airspeed indicator, there would be no ground speed indicators, no radar nor any other electro optical ranging devices.
The YB-49 was already jet powered https://en.m.wikipedia.org/wiki/Northrop_YB-49
Whilst not supersonic it’s quite possible that he could’ve encountered one of these too or another flying wing variant.
This quite frankly more plausible than aliens as an explanation, the time frame of the sighting matches the period during which the USAF was exploring a lot of flying wing designs and that it was also the first time that jet powered aircraft began to appear and when turboprops were reaching nearly transonic speeded.
So overall it’s very likely that what he saw was an experimental aircraft that was much faster than any aircraft that he encountered in the past and the slightest of errors in the estimation of size and range would have pushed any airspeed calculation into the supersonic range.
But if you're in the mood for conspiracy theories, Wikipedia's description of the end of the XB/YB series is pretty surprising as well: "Only two months later, all Flying Wing contracts were canceled abruptly without explanation by order of Stuart Symington, Secretary of the Air Force. Shortly thereafter, also without explanation, Symington turned down a request from the Smithsonian for the Air Force to donate one of these big wings to its collection of pioneering Northrop aircraft. All remaining Flying Wing bomber airframes, except for the sole YRB-49A reconnaissance version, were ordered chopped up by Symington, the materials smelted down using portable smelters brought to Northrop's facility, in plain sight of its employees."
(The motivation for this is supposed to have been contract favoritism, but it looks a lot more exciting if you accept the idea that there was of still-secret-to-this-day unreported flight testing happening in 1947 :)
[0] https://en.wikipedia.org/wiki/Northrop_YB-49#/media/File:YB4...