I'm struggling to understand the downvotes; this is a perfectly reasonable hypothesis - the LHB occurred between 4.1 and 3.8 billion years ago, the earliest evidence we have for life on Earth is from around 3.7 billion years ago. Admittedly 100 million years is a long time, but in geological timescales, there is the blink of an eye between Earth cooling enough to be suited to life, and life cropping up.
Since current theories, and experiments conducted since the '70s suggest that it is rather difficult to get life going on its own, it doesn't seem totally unreasonable to posit that if life can exist in a dormant state inside a frozen astronomical body such as a comet, then it would only take a small fragment of such a body surviving re-entry intact to deliver such life to a planetary environment.
We know primitive life can survive inside such an body, because such life can survive in more extreme environments on earth (frozen for millions of years under polar ice, or inside nuclear reactors). We also know that icy meteorites can survive partially intact when colliding with Earth - superheating of the outer layers 'cushions' the interior so that it does not melt.
Frozen solid inside half a kilometre of ice would also nicely protect any microorganism from the sort of hard radiation found in space, so it is not unreasonable to suppose that if such life found its way into the interior of such a body then it could survive. Of course, the question would then be 'how did it get there', and if we were to find evidence of life in such an environment, this would inevitably suggest that such life is commonplace and abundant in the universe, and raises the further question of its ultimate origin.
Anyway, my point is, that from a hypothetical point of view, none of this is beyond the bounds of reasonable possibility, unless you happen to subscribe to the 'Earth was created in 6 days' rubbish that the less rational amongst us spout.