Strangely, during those giant impacts in which Noachian Mars' surface would have been covered with a rain of molten lava making it hotter than present-day Venus, there would still have been refuges for microbial life to exist in: the subsurface, more than just a few dozen meters down. The calculations of Colaprete and Segura show that it would have stayed below the boiling point across most of Mars even during the most catastrophic episodes of raining lava and boiling surface water from giant impacts.

If Carr and Head are right and Noachian Mars' northern lowlands were filled with a fairly deep frozen ocean whose bottom layer was melted into a thin layer of liquid water by geothermal heat, this would have been another shelter for Martian microbes from the catastrophic surface environment -- for a lot of that thick ice layer would probably not have been melted or boiled away by the rain of lava even during a giant impact.

Indeed, although the oldest confirmed evidence of fossil life on Earth runs back only 3.5 billion years -- after the era of heavy bombardment had ended -- it's possible that bacterial life first appeared on Earth even during our own planet's period of equally vicious giant impacts.

The situation on Earth would have been different, thanks to the enormous heat-absorbing capacity of our planet's thick ancient water oceans. The impacts of asteroids big enough to sterilize the surface of Mars would have boiled away a few hundred meters of seawater from the top of Earth's oceans, but still leave a big reservoir of ocean water below the boiling point that could serve as a huge refuge for any "thermophilic" microbes capable of surviving hot water (such as still exist in large numbers in present-day Earth's hot springs)

But when Earth was hit (every few tens of millions of years) by an asteroid big enough to COMPLETELY boil Earth's oceans away, the existence of its big oceans would actually make things much worse than they would be on Mars after a comparably big impact. That vast cloud of steam would contain enough stored heat, and radiate it slowly enough back into space, to keep Earth's surface above the boiling point for thousands of years (rather than just a century or two as on Mars) -- and this would allow that killing heat to penetrate much more deeply into Earth's rocky crust than on Mars.

Any remaining non-boiling water in Earth's crust capable of sustaining living thermophilic microbes would have to be buried in the pores of rock more than a kilometer below the surface, much deeper than on Mars -- so deep that the heat from Earth's own interior would start to endanger the microbes. It isn't impossible that thermophilic Earth germs survived the biggest impacts to hit Earth during this era; but it would have been, on balance, a lot harder for them to survive than on Mars.