A close second is the period where the monkeys started wearing clothes, driving cars and programming computers.
“Far out in the uncharted backwaters of the unfashionable end of the western spiral arm of the Galaxy lies a small unregarded yellow sun. Orbiting this at a distance of roughly ninety-two million miles is an utterly insignificant little blue green planet whose ape-descended life forms are so amazingly primitive that they still think digital watches are a pretty neat idea.”
― Douglas Adams, The Hitchhiker’s Guide to the Galaxy
From memory, to get fossilised soft tissues you want the remains to be buried extremely rapidly in an environment where the soft tissues don't decay (typically an anoxic environment, so for a shale basically covered in mud). So a mudslide is one option, and I think there are some lovely fossils North American from the end of the Cretaceous that are hypothesised to have been buried by the tidal wave caused by the Chicxulub impact.
Edit: After some googling, the Cretaceous fossils I was thinking of is Tanis,[0] which is in fact plausibly (but not universally) thought to be covered by the earthquake caused by the impact, before the tidal wave arrived.
What does "modern" mean in this discourse?