A bit frustratingly, they mean "geologically instanteously" which is not the same as "instaneous as per human perception".
I'm not sure how long rock takes to cool after an asteroid impact, maybe days, maybe months or years depending on how large of an impact and how cold the surroundings (no atmosphere soooo....)
These mechanics are not discussed in the article and are instead just dismissed as "negligible"
Wouldn't molten rock simply flow and flatten? Even if not yet rigid, I'd assume the mountains do effectively form instantaneously (i.e. seconds or minutes), possibly flattening some as they slowly cool.
EDIT: The PBS NOVA special "The Day the Dinosaurs Died" describes the mechanics of the Chicxulub impact starting at about the 33 minute mark. It's as instantaneous as one would intuit, given the magnitudes involved:
> NARRATOR: The asteroid had punched a hole nearly 20 miles deep, gouging a crater 124 miles wide. Over 40,000 cubic miles of rock were displaced, rising into towering mountains.
> JOANNA MORGAN: So, this is an absolutely amazing event, because that happened in less than two minutes, and if you think of it, mountains the size of the Himalayas were formed in seconds.
> NARRATOR: As the mountains collapsed, they formed what's known as a "peak ring," found only in the largest of super craters. It's the only peak ring left on Earth; the next nearest is on the moon.
See, now this is an enjoyable fact. It is interesting to think that all of the forces involved in the collision will finish propelling themselves into each other within 2 minutes. One would think that it would be a little bit longer than that, because the transfer of energy between two cars in a car crash is over in a few seconds. But an asteroid colliding with a planetoid seems like it would take longer, given the amount of mass involved and the amount of deceleration that needs to take place (x km/s to 0.0000000 km/s)
Another cool fact: IIRC, the heat was so intense it basically incinerated all flora and fauna across distances that effectively encompassed most of the Americas. The rest of the planet burned more slowly, relatively speaking, as material fell back from outer space and forests burned in a planet-wide conflagration.
Flattening is a battle between gravity and a material's binding energy. The Moon's mass permits steeper slopes with similar material. (There are still limits, of course.)
Sorry, I didn't realize there was a paywall/geo-block. It works for me in Chrome Incognito after confirming that KQED is my local affiliate, so it might just be regional.
(I do donate to KQED, partly so I can access PBS TV on Roku, but account login is just... I don't have the words... so I don't actually login on my computer, and my Roku account link invariably, mysteriously deactivates sometime between the last time I watched something and the next time I want to watch something.)
This article is barely mentions formation of mountains on Earth. The article is almost entirely about lunar craters, lunar central peak craters, and lunar peak ring craters.
It's interesting how my mind had some trouble processing some of those crater images, because I saw initially some of them as circular buttons, going up from the surface, instead of craters going down.
I had to stop looking, and look back several times before my mind could actually see some of those pictures correctly.
It has happened to me since I was a child, at the time of Apollo. My trick was turning the photo upside down so the light aligned with the room source.
I can't imagine the size of object that formed the Valhalla crater on Callisto. The central region is 360km across, and the diameter of the entire basin is 3,800km. That's a distance on earth from LA to Arkansas!
Mountains on the moon (aka: crater walls) form nearly instantaneously because of a violent impact.
You can make instant mountains on Earth too. Downside is, it'll probably kill off most life on the planet.