Actually, the time for life to evolve is much shorter than 1 billion years.
After the earth formed, it was subjected to intense bombardment by smaller
bodies, and possibly had a collision with a Mars-sized body, resulting in
the formation of the moon. The surface was completely melted during this time,
until about 4.1 billion years. There are some possible rocks from this period
(embedded in younger rocks). The first sedimentary rocks are from 3.7-3.8
billion years ago. If you believe water was necessary for the origin of life,
only a couple of hundred million years pass between the first life and the
fairly sophisticated (ie., it already has a completel intermediate metabolism
and is probably photo or chemosynthetic) last common ancestor of all life.