We are in a vast, seemingly-empty universe. Models which predict the universe should be full of life should be penalised with a lower likelihood.

The only models which we can rule out are those which predict the universe is full of life which leads to long lasting civs which expand physically, use lots of energy, and rearrange on stellar scales. That's an enormous number of conjunctions/assumptions about future civs. Models where the universe is full of life, but life leads to tech singularities which end physical expansion (transcension) perfectly predict our observations, as do models where civs die out, as do models where life/civs are rare, and so on. . ..

But this is all a bit off-topic now because we are ignoring the issue I was responding to: the evidence from the timing of the origin of life on earth

If we find that life arose instantly, that is evidence which we can update our models on, and leads to different likelihoods then finding that life took 2 billion years to evolve on earth. The latter indicates that abiogenesis is an extremely rare chemical event that requires a huge amount of random molecular computations. The former indicates - otherwise.

Imagine creating a bunch of huge simulations that generate universes, and exploring the parameter space until you get something that matches earth's history. The time taken for some evolutionary event reveals information about the rarity of that event.