We have a fair amount of evidence. For one we know where it impacted, obviously such a large thing leaves a trace. Secondly based on the geologic record we can tell what followed the impact. The meteorite essentially caused a “nuclear winter”. People don’t realize this but the meteorite that killed the dinosaurs didn’t kill them in an instant on impact. What it did was drastically change the climate which made the Earth inhospitable to dinosaurs and they died out.
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