On Earth it would absolutely show up. Because Earth is tectonically active, and has an active atmosphere that erodes things in relatively predictable ways, alon

On Earth it would absolutely show up. Because Earth is tectonically active, and has an active atmosphere that erodes things in relatively predictable ways, along with a number of other processes that can date things, we'd be able to tell that there's a whole bunch of impacts that seem to have taken place at suspiciously close to the same time, even millions of years after the fact. If there's more than a couple of them, it may even be the case that it becomes clear that they were specifically targeted; e.g., 2/3rds of the planet is water, if we found 8 impacts on land or coasts at the same time and could show that there were 0 in the middle of the water, that would be very strong evidence for intelligent action, for which "military" is the most likely conclusion. In other environments, it may be much more difficult, but similar effects on more detailed scales may be in play. It's possible the space war was won with One Big Rock, but for a variety of reasons, I'd expect space war is more likely to occur with a variety of smaller rocks. Primarily, One Big Rock is harder to steer at militarily useful speeds, and you have to be pretty committed to wiping out not just your enemy, but the entire ecosystem. A lot of much smaller rocks would be more militarily useful in all sorts of ways, speed of deployment and redundancy being among the most important. If there is a war between a space-faring civilization and the groundpounders, the space-farers win if they just degrade the ground civilization to the point that they are no longer space-faring and unable to interfere. Spending the considerably greater resources to massively overkill past that goal is possible, but would not be the most likely outcome in my opinion because of the outsize expenditures and much longer time to return on said expenditure vs. smaller, more nimble attacks.