Is it considered a false dilemma because the chance theory appears to present only two possibilities, when in reality there could be many?

Now that you bring this up, I think the chance theory (or whatever it is called) forces us to make a choice/decision between extremes.

As it happens I’m writing a novel on the subject of the propagation of life. — Wayfarer

Wow! This is very intriguing!

I will keep the Forum posted, but only if I find a publisher.

If life were not only carbon based, I do think we would be right to expect more aliens. That said, if it is carbon based and only forms on planets similar to Earth, most of those planets are either still forming or are young compared to Earth, meaning we would not expect there to be ETI, or at least not that many ETIs; so I agree that some pessimism is warranted in that regard, but not about the possibility of ETI. — NotAristotle

I don't think anything warrants that level of certainty. I have not seen any analysis that we can say that the earth is exceptional in how early it formed.
The only requirements I am aware of are a third-generation star and icy comet impacts. Even assuming these are mandatory requirements (which is debatable), it still leaves a window billions of years wide, including billions of years before the Earth formed.

The timescale on when an ETI would be expected to send out a radio signal will consider 1. the odds of abiogenesis, and as ↪Wayfarer pointed out, 2. the times at which those planets formed. — NotAristotle

I wouldn't get too focused on radio signals. Yes, SETI and other organizations look for radio signals because what else can we do? But in the context of the Fermi paradox I think it is wrong to see it as requiring ETIs to be broadcasting a radio signal at just the right time for us to look.
For the Fermi paradox, we're talking about anything detectable, so that would include things like replicating probes spreading to our star system, and megastructures like Dyson spheres, both of which could persist in some form long after a species has gone.

And, importantly, it includes technology that we can't understand. What I mean by that is, we don't have to suggest that advanced species will make Dyson spheres. Maybe the most important technology for a million years+ advanced species is a giant helix, that radiates X-rays intensely, for reasons we couldn't possibly understand yet.
Well, we don't see that either. We don't see anyone absorbing, emitting or refracting EM radiation on a large scale anywhere.

Of course, it doesn't prove anything. But, given that there's no reason that we yet know of that the sky couldn't have been lit up with the lights of a million species, it's not a positive data point.

We do not know how life formed or whether other Earthlike planets have the conditions to enable life to form. The odds seem to be: what are the chances of all the right ingredients being in the right place at the right time? In another sense, there may not be any "odds" involved, it is either going to happen on another planet or it will not as a result of the atomic, chemical, (whatever else), forces involved. When I say the "odds" I am referring to the credence we attribute to the result of life arising on another planet that is like Earth. So it is not so much that the process of life forming is random, but that our knowledge of whether another planet will or will not give rise to life is chancy. Or, to try to narrow it down a bit further, maybe the question of "odds" is really a question of just how similar other planets are to Earth, the closer the similarity, the more likely the chances of life on that planet.

Most Earthlike planets are estimated to have yet to be born -- https://science.nasa.gov/universe/exoplanets/most-earth-like-worlds-have-yet-to-be-born-according-to-theoretical-study/ . <a href="https://assets.science.nasa.gov/content/dam/science/missions/hubble/releases/2015/10/STScI-01EVSR5F1P8JVARK199WAZPNBQ.pdf" target="_blank" rel="nofollow">https://assets.science.nasa.gov/content/dam/science/missions/hubble/releases/2015/10/STScI-01EVSR5F1P8JVARK199WAZPNBQ.pdf</a>

If this estimate is correct, and if it is also correct that life is carbon-based only, and if life only arises on some Earthlike planets but not all, then the fact that most Earthlike planets have not formed yet suggests that, as you said initially, we are one of the very first intelligent species. But I see no reason to reject the hypothesis that abiogenesis can happen on other planets. You are right that the timeline of discovery might be more like billions of years; that is a matter of when the other Earthlike planets form. (So my initial lower bound estimate of at least a 20,000 years waiting period for alien contact might have been an underestimate).

I see your point about detecting (or not detecting) other alien technologies. Given that the chances of ETI are low in my opinion, I think it unlikely that Dyson spheres or anything like that will be detected; at least, not in our lifetime.

Or, to try to narrow it down a bit further, maybe the question of "odds" is really a question of just how similar other planets are to Earth, the closer the similarity, the more likely the chances of life on that planet. — NotAristotle

I agree.

Now that we got to this point, I think it is worth asking ourselves: would they (the civilisations of an Earth-like planet) show themselves to us if they were capable of doing it?

Furthermore, what if it is actually better for us and for them that our paths haven't crossed yet?

haha, yeah I was thinking that myself, and I think it is a good question. It would seem to have to do with the evolution of that species and how risk adverse they are, or perhaps, with how communicative they are. If they are less communicative and more cautious like (I don't know turtles hiding in a shell?) then maybe they will refuse to broadcast any signals. Of course, if nobody broadcasts then the chance of any communication plummets.

Walk me through better to not have crossed paths; why would that be so?

Of course, if nobody broadcasts then the chance of any communication plummets. — NotAristotle

This is ture. Indeed, there is a positive aspect to that assertion.

Walk me through better to not have crossed paths; why would that be so? — NotAristotle

Understandable. Perhaps the rest of the civilisations on the Earth-like planets are thinking the same thing right now. We always tend to select the cautious choice.

If this estimate is correct, and if it is also correct that life is carbon-based only, and if life only arises on some Earthlike planets but not all, then the fact that most Earthlike planets have not formed yet suggests that, as you said initially, we are one of the very first intelligent species — NotAristotle

The cite doesn't really support the conclusion you're drawing though.
Yes, in a relative sense we might be "early" but even that tentative estimate still suggests around a billion rocky worlds before ours. And that's just in our galaxy.