I think we can see where different complex animals split in their evolutionary tree - so humans and starfish split a long way back. Then we use a standard mutation clock to estimate how long ago that was. If all complex animals split from simple animals an estimated 700m years ago...
>>> 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?