Had Earth lost the Moon early, would we be able to determine it once had a companion?

Question

Despite the Solar System looking quite stable, clockwork-like on human timescales, to such a degree the movement of its members is used to track time and make calendars since antiquity, it is pretty chaotic on longer timescales, of several million years. For example, recently there was news about a study(1), where researchers determined that close-passing stars alter our entire planetary system's orbital evolution via their gravitational perturbations on the giant planets, making retrodiction of past orbital evolution very uncertain beyond ~50 Myrs ago. Another example, for the future, was a study from 2009(2) that raised the possibility of Mercury eventually running amok, causing destabilization of all the terrestrial planets about 3 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth (although not likely. the probability of a large increase in the eccentricity of Mercury required to kickstart it was estimated about 1%, and the simulated orbit that lead to collision with Earth appears to be a single event out of a sample of 2,501 solutions).

Given these possibilities, I think that, beyond scenarios involving a direct collision with Earth, one can imagine a near miss situation, where our planet narrowly avoids a direct hit, but the Moon is lost, say either shattered, ejected from the solar system, or plunging into the sun. So I ask, assuming this actually happened at some point between Solar System formation and now, and somehow humanity still managed to arise on this planet, would we be able to determine Earth once had a long lost companion?

References:

(1). Kaib, Nathan A., and Sean N. Raymond. Passing Stars as an Important Driver of Paleoclimate and the Solar System’s Orbital Evolution. arXiv:2402.08734, arXiv, 13 Feb. 2024. arXiv.org, https://doi.org/10.48550/arXiv.2402.08734.

(2). Laskar, J., and M. Gastineau. “Existence of Collisional Trajectories of Mercury, Mars and Venus with the Earth.” Nature, vol. 459, no. 7248, June 2009, pp. 817–19. www.nature.com, https://doi.org/10.1038/nature08096.

Answer 1

The collision between the Proto-Earth and "Theia", the hypothetical planet responsible for the Moon's formation, is thought to have given us the essential elements for life to form, since it brought the appropriate materials which Earth might have otherwise been deficient in from a different region of the protoplanetary disk. Without this collision, life on Earth as we know it might not exist.

The Moon also significantly influences Earth's tides, which in-turn stabilized Earth's climate by redistributing heat, allowing the planet to be globally habitable.

Now, to answer your main question: if humans formed without a moon, whether we could tell if we initially had one or not depends on a few factors, such as how long it lasted. As aforementioned, the Moon plays a huge role in our ocean's current. With that in mind, if it was around for long enough, it should have had enough influence to create certain anomalies in fossils formed by tides that couldn't otherwise be explained, just to list one example. So yes, there would very likely be some clues.