Not certain at all, it’s based on last universal common ancestor estimates(LUCA) and supported by (lack of) fossil record.
>When it comes to direct evidence of an industrial civilization—things like cities, factories, and roads—the geologic record doesn’t go back past what’s called the Quaternary period 2.6 million years ago. For example, the oldest large-scale stretch of ancient surface lies in the Negev Desert. It’s “just” 1.8 million years old—older surfaces are mostly visible in cross section via something like a cliff face or rock cuts.
While I think its highly unlikely (I mean less than 0.00001% possible) the means in which we would could even detect it are complicated
[0]: https://www.theatlantic.com/science/archive/2018/04/are-we-e...
I thought the Cambrian Explosion's fossil record was pretty sizeable - in fact, it's named after the place where the fossil layer was first discovered. I didn't know it was related to a common ancestor. Are you thinking of something else or am I missing something major?
>>> Complex animal life took 3.5 bn years to emerge on Earth,
>> How certain are we it took that long (the first time)?
> Not certain at all, it’s based on last universal common ancestor estimates(LUCA) and supported by (lack of) fossil record.
Do you mean, there's little evidence of pre-Cambrian absence? Absence of evidence is some evidence of absence, in this case.
But how does LUCA fit into this question?