It turns out my friend had put a LOT of thought into this exact question. Enough to do a masters in geology, his work ultimately making it into a high profile journal with writeups in places like the NY Times.
He started talking to various geologists about what might survive as telltale markers of our civilization. Buildings or structures of any sort? Ha! Statues and monuments? Maybe we’d notice the odd deposit or two of minerals.
After going through a long list of candidates, he settled on carbon cenospheres. These are little balls of carbon almost exclusively made in internal combustion engines as the result of aerosolizing fossil fuels. Sixty million years ago, our love of the ICE will show up in the fossil record as a light dusting of cenospheres covering the earth—contemporaneous with massive numbers of species going extinct due to mankind’s other influence.
And as my friend was telling me his story, this is where my hair stood on end. Sixty million years ago we see a massive species extinction... and a light dusting of carbon cenospheres covering the globe.
But we also see unnatural levels of iridium at the same point. And, while it’s hypothetically possible some industrial civilization was mining iridium and blanketing the globe with it, it’s more probable that the iridium was delivered by an asteroid.
But how would you know? So my friend, as part of his research, went taking samples of his cenospheres from around the globe. What he found was interesting: namely, the further one gets from the Yucatan (where scientists had already validated there was an asteroid strike), the cenospheres get smaller. The big heavy ones precipitated out of the air closest to the Yucatan asteroid strike. Hardly likely to be coincidence.
So much for ancient civilization this time around.
However, his work rewrote a critical understanding of the KT asteroid extinction event. Namely, we previously thought most of the carbon at the KT boundary was the result of giant forest fires ignited by the strike. However we now know that the strike must have aerosolized massive oil fields under the Yucatan at that time and set them ablaze.
Not a bad contribution to science starting from a sci-fi premise!