For all we know, life started on Mars, not here. Hence the "sudden explosion" of life.
Early on I would expect a whole lot of "horizontal gene transfer" sort of things to have taken place. So for example in addition to actual horizontal gene transfer, there are mechanisms like one organism enveloping another to eventually become organelles, co-opting products from each other, etc. All of which would act to homogenize life and make certain process ubiquitous.
Finally, there's an outside chance that "there's only one way to do it".
Diversity could exist in harmony and the lack of any diversity is a pretty strong signal that the only extant version is either very rare or the only to ever emerge.
Everything in nature is diverse except RNA/DNA and this fact alone is a sort of evidence.
Or RNA was just a winning virus that infected all other life or killed all competition to make it seem like there was only one origin.
Absence of evidence is not evidence of absence.
When you should see evidence but don't, "absence of evidence is not evidence of absence" doesn't apply. Otherwise absence becomes unprovable à la Russell's teapot.
By comparison, we’ve looked nowhere (Earth is big and mostly inaccessible to humans) and don’t know what we should be looking for, since we don’t have any testable models for the origin of life yet.
And re RNA I was just giving one example of why all life might have it (ie RNA gave an evolutionary advantage so anything without RNA died). There’s all sorts of reasons why we don’t have evidence of multiple origins, not least of which is that we just haven’t looked in the right place and there could easily be life being created from scratch on this planet without even knowing about it. That’s what the entire field of synthetic biology is even about; just doing it in a lab instead of out in nature so that we can understand the conditions better.
This is about a quarter of the lifetime of the universe ago, and we don’t have any evidence at all that life has ever occurred in any other way. We’ve only really been looking for a hundred years or so, but we’ve not found any “fountain of life” where life is being created, we’ve not found evidence of any type of life that isn’t broadly related.
I absolutely agree that it’s not evidence, but I believe that on balance, it makes more sense to take our working hypothesis to be something that fits the evidence we do have, rather than believing the evidence must exist we just don’t have it.
To be clear, I’m not advocating that we don’t investigate both possibilities, and I wouldn’t put much weight behind my own guess here.
And you’re right, assuming those fossils even managed to survive in the first place and not get destroyed. And that’s ignoring that early life would have been microscopic and we wouldn’t really see fossils of that.
But even if it did, one clear argument could be that the conditions on Earth when it happened would have been very very different than the earth today. Lots more volcanic activity, lightning storms, and UV radiation. We don’t know the exact conditions needed to create life from inorganic precursors so we don’t have a solid hypothesis of was there multiple origins or a single or is it still happening today.
But given we have the beginnings of evidence of life on Mars, Titan, and Triton, and that it would make sense since we know life must arise naturally out of non-life origins (since there was no life at the Big Bang), I would venture to guess that life is both rare and common. Intelligent life also seems common although less common than life overall (other primates, dolphins, Elephants, ravens/crows, and cephalopods are all quite intelligent). Intelligence + tool use is also not uncommon but rarer (we’ve caught animals on tape using tools). Advanced industrial civilization is the only thing so far that we only have a single existence evidence for - is that unique, can there ever only be one on a planet at a time, or can there only be one ever when conditions are right? Eg we wouldn’t have gotten very far if we were on the planet earlier and didn’t have dinosaur bones to power our industry with - the jump from whale oil to nuclear/photovoltaics/wind turbines seems unlikely but maybe it would happen anyway, just longer.
Life increases entropy and doesn't break 2nd law of thermodynamics.