One huge problem with your argument is the timescale. True, we don't see evidence of other intelligences probing and reporting on us. But you're talking over a 4.5b year timescale for this planet, and we're a very short-lived life form on those timescales. If you wanted to keep tabs on a planet forming you might check it once every 0.5m years. Close investigation might be once every 100,000 years. Why should we expect to see something in the time we have been looking - about 100 years? Or, if you only count the SETI monitoring, about 30 years...
Missed this earlier DG. In a sense you are correct regarding timescales but again, you are with respect, looking at it from the wrong angle. SETI is looking for a needle in a haystack. It hasnt one single candidate signal in nearly 40 years. It hasnt even come close to anything either despite one or two supposed candidates. The 'Wow!' signal is interesting but was never picked up by the second Big Ear sweep just seconds later. It has no standing within the SETI or scientific community.
We shouldnt be looking for alien lifeforms looking for us. There are major flaws with this.
As you say, time. Who in their right mind would observe a planet for half a million years never mind 1, 2 or 3 billion years? That lifeform may not exist much beyond a million years before some catastrophy wipes it out.
In all of space, why would an intelligent lifeform look in this direction for such time?
Then there is the sheer number of stars and potential planets out there. Even we have detected nearly 400 exoplanets. An intelligent lifeform would have better planet hunting techniques so they would find many many more planets. The chances of them spotting earth in that lot would be similar to SETI finding a candidate signal ie virtually none.
We have no technology of note that makes this planet stand out to any intelligence seeking other intelligent lifeforms. It was until recently assumed our radio transmissions would expand beyond the earth at the speed of light. Thus, our earliest radio transmissions should be roughly 100 light years away from us in all directions. However, it transpires the radio and now more powerful tv signals all but disappear into silence at about 5 light years distance.
This is why SETI will
never pick up an alien transmission. Any alien would need to point an incredibly powerful narrow beam transmission in our direction to be detected even at the hydrogen frequency 1420Mhz loved by SETI.
Our approach should be one devoted to looking for alien artefacts since older intelligent life would be more technologically advance. Advanced to the point of making their technology stand out. For example a dyson sphere. A dyson sphere is when a lifeform encases its star and planet's orbit so as to capture all the star's energy. Dyson spheres would be enormous and easy to spot.
Fermi's paradox is that the galaxy is teeming with intelligent lifeforms but where are they? By definitions, many if not most of those lifeforms will be older than us since humans have only been around for a short time. Given the accepted age of the galaxy (roughly 10 billion years), even travelling a sub light speed, one lifeform could colonise the entire galaxy in less than 10 million years.
That gives them plenty of time to repeat the feat many times over. If that had happened, we should easily see evidence of many other intelligent lifeforms either existing now or having existed and died out.
We see neither. The only logical conclusion based on the weight of evidence is, we are the first intelligent lifeform in the galaxy, we are the most technologically advanced lifeform in our galaxy right now.