Life arose on Earth really fast after the surface stopped being magma. Since Mars cooled down faster the idea is that it could have spent 100 million of year developing bacteria which were then seeded the Earth as soon as there was liquid water there.
While in general the argument may hold that life evolved too fast, your numbers are off. 100 million years is just about the minimum estimate for the emergence of life on Earth. If Mars has a longer timeline it should be closer to 1 billion years between solidification and emergence of life.
You're right that my numbers are off. I'd bee thinking of the end of the Late Heavy Bombardment 3.8e9 years go, but there's some suggestive evidence there was liquid was on Earth's surface 4.4e9 years ago. And the earliest bacterial fossils are from 3.5e9 years ago, though goodnesss knows how long it took bacteria to make colonies that ended up making fossils to survive to the present day.
