Current theory suggests that the non-avian dinosaurs died out at the KT event at 65M years ago. The big boom in mammals including, notably, primates came after the PEMT, around 55M years ago. The first human-like ape (Homo Erectus) was 1-2m years ago and the first Homo Sapiens was 100k-200k...
There's quite a bit of evidence that some meteorites have carried Amino acids with them. https://www.nasa.gov/topics/solarsystem/features/dna-meteorites.html
Combine Amino acids and you get DNA. It's not impossible that the origins of life may have been seeded/catalysed/accelerated by...