There are two possible ways such an object might have been launched from Earth into a heliocentric orbit. One is being propelled by an explosive volcanic eruption. Volcanic eruptions release plenty of energy—far more than needed to accelerate an object to escape velocity—Mt St Helens was estimated at around 24 megatons, more than any hydrogen bomb tested by the U.S., but I am dubious of the mechanism that could concentrate enough of that energy in a rock to cause it to escape. The other mechanism, which I believe is much more probable, is secondary ejecta from an asteroid impact. We have found meteors on Earth which are known to have originated on the Moon and Mars (isotope ratios provide indisputable evidence of this), and it’s almost certain they were ejected by impacts on those bodies. It’s harder to escape the Earth due to its stronger gravity and thick atmosphere, but then asteroids have energy in abundance, coupled with hitting faster than escape velocity.
Check out the “manhole cover to the stars” from the Operation Plumbbob Pascal-B nuclear test on 1957-08-27. If it made it through the atmosphere without burning up (probably not), it was estimated as travelling six times Earth’s escape velocity and may have escaped the Sun’s gravity onto an interstellar trajectory.
Any object orbiting the Sun in an orbit similar to the Earth’s has a high probability of eventually hitting the Earth or Moon. Every time it passes close to either, their gravity perturb its orbit and eventually it will be captured into an unstable orbit in the Earth-Moon system and either escape back to a heliocentric orbit or hit the Earth or Moon. A famous case of this is the third stage of the Saturn V rocket that launched Apollo 12 toward the Moon. See “The Strange Voyage of Apollo 12’s S-IVB Stage”, posted here on 2023-01-26. Launched from Earth in November 1969, it eventually went into orbit around the Sun where it remained until September 2002, when an amateur astronomer discovered it orbiting the Earth. It had been perturbed into an unstable orbit while passing the Earth-Moon system. It escaped again in June 2003 and is now back in orbit around the Sun. It may next be captured sometime in the 2040s. It is almost certain to eventually hit the Earth or Moon, but it may take millions of years before this happens.