>>> 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?