Not really. Very large improbabilities require a lot more time than what the universe has been around for.

From our limited sampling, it happens with some measurable frequency.

Going from zero to one of something tends to be a lot less likely than going from one to two or more.

Yea but we don’t know how many failed attempts there were that got stuck at zero. We only know our one existence. Could be trillions of dead universes before ours.

Yes really. These improbabilities are guesswork, and their size is unknown. We know a spacefaring civilization has happened once, so the probability is far greater than you allow, and time obviously sufficient.

I think the only real quibble I’d have here is:

It is clearly possible to have a space-faring civilization, we’ve seen one. But the density could be extremely low. Fine, in infinite space we’ll get an infinite number of spacefaring civilizations whatever the odds. They exist, we just might never interact if the density is low enough.

But, I’m not sure, maybe it is a philosophical question or maybe it is a physics one (I only had an engineering education so at the extremes these get hard to distinguish sometimes). Does the universe outside of our light cone “exist” in some sense? If not, then I guess the universe is not quite so big.

Further, you might suppose that the planet needs to be in some reasonable band, in terms of power being absorbed from the star, to be amenable to life. And that, in order to hit spaceflight, you’ll need to have accumulated a certain amount of energy (for rocket fuel). This could bound the beginning of space-flight-viable planets to those which have already had a good amount of life for a couple hundred million years.

So this would seem, to me at least, to limit our universe of possible planets to those that are more than a couple hundred million years old, at least, in our frame of reference, right? (and this is assuming most of the Precambrian was a waste of time that could be skipped through lucky evolution).