The evidence is in the hollow-eyed face of the man in the Moon: a wave of asteroids showered Earth and the Moon in the distant past. They scarred the lunar surface with vast, circular impact basins and wreaked even greater havoc on our planet, which presented a bigger target.
It was originally thought that the Late Heavy Bombardment (LHB) of asteroids came after the initial creation of the planets and lasted from 4.1 billion to 3.8 billion years ago. But it is now thought that Earth was still suffering from regular blows as early as 2 billion years ago.
This was a key period in early evolution, which saw the split of the single-celled organisms called archaea from bacteria, and the rise of photosynthesizing cyanobacteria. How life would have responded to a sustained barrage throughout this period is unclear. Learn more here or here.