This is only a partial story.
But still, quite interesting idea.
How fast did an object have to hit the earth,
to blast earth into space?

Was it Jules Verne that wrote a book about this,
"Off on a Comet" ?

yes,
Off On A Comet: Verne, Jules: 9781481853538 - Amazon.com
Amazon.com
https://www.amazon.com › Off-Comet-Jules-Verne
Wikipedia
https://en.wikipedia.org › wiki › Off_on_a_Comet
Off on a Comet (French: Hector Servadac) is an 1877 science fiction
novel by French writer Jules Verne. It recounts the journey of several
people carried ...

from
https://www.newscientist.com/article/2381928-meteorite-left-earth-then-landed-back-down-after-round-trip-to-space/

Meteorite left Earth then landed back down after round trip to space
Most of the meteorites found on Earth come from asteroids, but a few
come from other bodies like Mars and the moon. Now, researchers say they
have discovered a new kind - a rock originally from Earth that went to
space then came back

By Alex Wilkins

11 July 2023

The meteorite NWA 13188 seems to have travelled to space and back

Albert Jambon

A meteorite found in the Sahara desert in Morocco may have originated on
Earth, before being blasted into space and returning from orbit
thousands of years later. If confirmed, this boomerang space rock would
be the first of its kind we know about.

Almost all the meteorites we have found come from asteroids, but a tiny
fraction are from planetary bodies, such as Mars and the moon. These
come from violent impacts that launch debris into space before …

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"a425couple" wrote in message news:ZBArM.340585$fNr5.118073@fx16.iad...

This is only a partial story.
But still, quite interesting idea.
How fast did an object have to hit the earth,
to blast earth into space?

-----------------
The minimum velocity for a low Earth orbit is about 7.8 km/Sec. Above 11.2
km/Sec an object will escape Earth's gravity and orbit the Sun. The ratio
between them is the square root of 2, a fairly small window. Meteors have
arrived at as high as 70 km/Sec, so far. Otherwise everything depends on the
fraction of energy transferred as velocity versus destroyed in fracturing,
and velocity lost to air resistance which can be huge. Colliding billiard
balls transfer energy efficiently but rocks shatter.

https://en.wikipedia.org/wiki/Space_gun
A serious complication is that an uncorrected orbit will try to pass back
through its launch point. Rockets start vertical so they won't tip over and
then curve into the direction of the orbit.

In college Physics a homework problem was to calculate the return time of a
weight dropped into an evacuated well that passed clear through an Earth of
uniform density. The tricky part was finding a formula to integrate that
compensated for depth. It turned out that if you are anywhere within a
uniformly thick hollow shell its gravitational attractions in any pair of
opposing directions cancel to zero, i.e. you float weightless. You are drawn
toward only the mass in the sphere below you. They left that for us to
discover mathematically. Also the return time equals the period of a low
orbit.

https://www.thenakedscientists.com/forum/index.php?topic=46531.0

https://en.wikipedia.org/wiki/Dyson_sphere

https://en.wikipedia.org/wiki/Ringworld

On Thursday, July 13, 2023 at 8:31:43 AM UTC+10, Jim Wilkins wrote:
> "a425couple" wrote in message news:ZBArM.340585$fNr5....@fx16.iad...
> This is only a partial story.
> But still, quite interesting idea.
> How fast did an object have to hit the earth,
> to blast earth into space?
> -----------------
> The minimum velocity for a low Earth orbit is about 7.8 km/Sec. Above 11.2
> km/Sec an object will escape Earth's gravity and orbit the Sun. The ratio
> between them is the square root of 2, a fairly small window. Meteors have
> arrived at as high as 70 km/Sec, so far. Otherwise everything depends on the
> fraction of energy transferred as velocity versus destroyed in fracturing,
> and velocity lost to air resistance which can be huge. Colliding billiard
> balls transfer energy efficiently but rocks shatter.
>
> https://en.wikipedia.org/wiki/Space_gun
> A serious complication is that an uncorrected orbit will try to pass back
> through its launch point. Rockets start vertical so they won't tip over and
> then curve into the direction of the orbit.
>
> In college Physics a homework problem was to calculate the return time of a
> weight dropped into an evacuated well that passed clear through an Earth of
> uniform density. The tricky part was finding a formula to integrate that
> compensated for depth. It turned out that if you are anywhere within a
> uniformly thick hollow shell its gravitational attractions in any pair of
> opposing directions cancel to zero, i.e. you float weightless. You are drawn
> toward only the mass in the sphere below you. They left that for us to
> discover mathematically. Also the return time equals the period of a low
> orbit.
....

An interesting problem.
Stat mech suggests something like a Bolzman distribution
would explain the speed distribution
of particles from an asteroid impact.
And my back of the env shows if it had an impact speed around 2.5 kps then 60 parts per million of the blast could reach around 4 kps and get to a substantial height.

But speed is not the only factor. The infamous space gun threw a projectile -- actually a long metal rod about 1" in diam and mass of several hundred pounds --
around 4 kps at the muzzle to get up to 100+ mi alt.
The object had to be long and thin ("planing hull") to withstand the
atm drag on the way up.

So the whatever impact that created the ibject in question had to get it moving fast enough,
in the right direction, and it had to
have the right shape to make it past the
atm.