First billion years after Earth started to form there were so much debrie in Solar system, that under frequent shelling by huge rocks and other forming bodies Earth did not even have a chance to cool to liquid water temperatures yet.
Remember that Mars-sized body which slammed into Earth about 1/2 billion years after Earth itself started to pile up - and that this impact alone yeilded in energy release of the order of 1031 Joules - (that is about 1015 = one billion millions hydrogen bombs set off in less than a minute of collision duration) all over the globe.
Computer simulations show that in such collisions the globe (Earth) actually seases to exist - instead of two colliding bodies there is one fireball quickly expanding in size well beyond present Moon's orbit spilling around chinks of molten lava and debrie of all sizes, and then gradually cooling, contracting and settling as one bigger molten body and thick system of equatorial rings of orbiting debrie).
By the way, that is when and how Moon itself was formed as a by-product of such collision. That is also when Earth is believed to get its nice 23 degree axis tilt as a reminder of magnitude of a collision (due to which we have seasons, by the way - so they may be considered a gift of Satan instead of God).
Anyway, collisions of similar and smaller magnitude were common in the first billion years of Earth pile-up (that is how you make a planet after all - accumulating falling stuff). Gradually Solar system becomes more and more clear, but even now we still have enough debrie to obliterate life (50 - km rock is considered to be enough).
Now, the earliest recorded fossile life found on Earth is dated about 3-3.5 billion years ago - shortly after frequency and magnitude of those collisions were less catastrophic. Yet even after that life on Earth was almost obliterated (extinctions) many times by less catastrophic collisions.
So, it is completely incorrect that life "suddenly" emerged about 1-1.5 years ago. It emerged as quickly as small areas near poles on hot Earth cooled down to below water boiling temperatures (to sometimes be quickly obliterated by next asteroid the Solar system was so full back then.)
So, primitive life was actually extremely persistent on early Earth - it was probably rizing out of ashes many times - like mythical Phoenix, again and again at first possible opportunity.