Indeed, it's been theorized by many that life actually started at the deep sea hydrothermal vents. It's rich in energy, metals, etc. Even if not started there

Indeed, it's been theorized by many that life actually started at the deep sea hydrothermal vents. It's rich in energy, metals, etc. Even if not started there, there was a period where nearly the entire planet was under ice, and might have acted as a reservoir. On the scale of billions of years the earth spun more quickly, and the moon was significantly closer (and reflected more light on earth). Seems reasonably to expect there where more volcanoes, more hydrothermal vents, more earthquakes, and more tectonic activity of all kinds earlier in the earths history. Not to mention early in earth's history the late heavy bombardment. All making potential hospitable environments even if the earth was on average cooler than ideal. On the flip side the moon is going to keep getting further from the earth, as energy transfer via tides increases the moons velocity ... until 1 day = 1 lunar month. Thus the need for occasional leap seconds as the earth spins more slowly. Afterwards the moon will slowly decrease it's orbit because until it kits the Roche limit and turns into a ring ... unless the sun expands enough before then, which is the time scale of these changes.