Yep, the [paper's conclusion](
https://ntrs.nasa.gov/api/citations/20200000027/downloads/20...) was just as you said, there'd not be much of a record to find for civs older than 4 Ma. Also, there are past anomalous and abrupt events in the geological record that appear similar to byproducts from our anthropogenic activity. Evidence against is that timing for majority of such anomalous events can be matched to mundane geological activity in the record.
The rate at which we're accumulating change compared to geological record is also a strong argument against, although they argue limitations in current dating methods reducing how much can be said with certainty about prior epochs.
While there is precious little reason and evidence to believe a priori in a previous advanced dino civ, there are studies that could be done on sediment data that'd lend more certainty (such as looking for unusually rapid metal production).
> Anthropocene layer in ocean sediment will be abrupt and multi-variate, consisting of seemingly concurrent-specific peaks in multiple geochemical proxies, biomarkers, elemental composition and mineralogy. It will likely demarcate a clear transition of faunal taxa prior to the event compared with afterwards. Most of the individual markers will not be unique in the context of Earth history as we demonstrate below, but the combination of tracers may be. However, we speculate that some specific tracers
that would be unique, specifically persistent synthetic molecules, plastics and (potentially) very long-lived radioactive fallout in the event of nuclear catastrophe. Absent those markers, the uniqueness of the event may well be seen in the multitude of relatively independent fingerprints as opposed to a coherent set of changes associated with a single geophysical cause.
My opinion is this ultimately boils down to how hard human level intelligence is to evolve, which is why the hypothesis is interesting in the context of the Fermi Paradox. Intelligence might be extremely difficult to evolve, it might require an unusual background environment set of condition or just might not be that useful in general.