One of the most important discoveries of Unified Science is the finding of the active role of primordial Mars in the formation of our great Moon. It seems quite obvious to me that not all of the ejecta mass from the collision of the rest of Proto-Mars with Proto-Earth was able to reassemble into the newly forming moon.
Some fragments of this mass must have remained. Therefore, my second observational (and computational) suggestion for astrophysics is to check which of the so-called Near-Earth asteroids we know today could be the remnants of this process of Moon formation.
In Wikipedia we can read: "The first of these unusual minor planets to be discovered, number 433, was the dumbbell-shaped Eros in 1898." Various sky search programmes have found several similar objects. I suspect many of them are the "little children" of the 3.5 billion year old collision. At least their orbits and density of mass (see Wikipedia: "Near-Earth asteroid" and "(433) Eros") are strong arguments in favour.