The earliest fossils are bacterial mats at a couple of billion years ago. But this article goes into single bacteria life as far back as 3.5 billion years. So life appeared quite quickly after the water finally condensed. As they push back farther and farther, it supports the concept that DNA life was 'seeded' from afar. My general thought is that organic molecules would take a billion years or so to evolve to bacteria, maybe more.
The concept of a seeder means that somewhere else had those extra billions of years to coagulate the primordial soup. Or maybe not.