[sreevisakh]

I am also not an astrophysicist, but here is what I have read. Every planetary body has an imaginary envelope called the Roche limit [1]. For Earth, this is about 18,000 km in radius. Debris inside this radius will tend to get ripped apart, while those outside tend to coalesce. This is not due to gravitational instability or chaos. This can happen even if the gravitational field is be assumed to be uniform. (Earth's gravitational field has some non-uniformities due to non-homogeneous density of the planet. But I doubt it has any role in preventing debris from coalescing. More uniform, but heavier bodies like Saturn tend to rip debris apart even more).

What really rips smaller bodies and debris inside the Roche limit is tidal forces caused by gravity-gradient. Imagine a smaller body like a satellite or a comet. The region of that body closest to the planet will be subjected to greater gravitational force and acceleration than the region farthest from the planet (gravity-gradient). If the satellite/comet's self-gravity and material strength is not strong enough to resist this differential pull/acceleration by the planet's gravity, it gets ripped apart. This is roughly the concept of Roche radius.

In case of the giant impact hypothesis, the ejecta that coalesced into the moon was certainly outside the Roche limit. Ejecta with sub-orbital velocities would have fallen back onto the planet surface shortly. I am not sure what happened to the material that was in orbit inside the Roche limit. There is another phenomenon at play here - called tidal acceleration [2]. You may be aware that the moon is slowly moving away from Earth. This is due to tidal acceleration.

Tidal acceleration causes large objects (like the moon) outside the planet's geosynchronous orbit to slowly accelerate and move away. In case of the moon, it's Earth's tides that drag moon like this. Conversely, the objects inside the geostationary orbit tend to get decelerated and pulled into the Earth's atmosphere. I am not sure how strong this effect is for small and distributed objects like planetary debris. But that may be why Earth has no ring. It may also be that those small bodies were too close and drag from Earth's thin atmosphere may have pulled it back to the planet.

The moon is believed to have been very close to Earth (a few tens of thousands of kilometers) at the time of formation. The impact is also believed to have sped up Earth's rotation a lot (reducing the length of the day). This means that the geosynchronous orbit would have been much lower and likely below where moon was back then. Tidal acceleration slowed down Earth's rotation and elongated the day, just as it raised moon's orbit.

[1]: https://en.wikipedia.org/wiki/Roche_limit

[2]: https://en.wikipedia.org/wiki/Tidal_acceleration