If just .001% of 10 billion Earth-like planets orbiting sun-like stars in the Milky Way have harbored advanced, intelligent life, shouldn’t we have seen some kind of evidence of their past existence, since this would equal 100,000 civilizations?

Great question! Complicated answer. Let’s start by looking Earthward at ourselves, then we’ll compare that looking spaceward toward the stars.

As you know, homosapiens are the advanced, intelligent life form on Earth which is now technologically advanced and space faring.

Now by some estimates, humans have been on this planet only for the last 200,000 years, or one fifth of one million years. There are a thousand million years in a billion years, and the Earth is about 4.54 billion years old. So, humans have been on Earth for only a tiny fraction of Earth’s existence. Here’s a graphic to illustrate that point and more to follow below.

This image illustrates what it would look like on a 24 hour clock comparing the age of Earth to the presence of humans. In fact, life itself has existed on Earth for less of half the lifespan of the planet, what to speak of humans.

So you can see, even though we have a planet in the goldilocks orbital region around our sun, someone looking at Earth many light years away would not see humans even though humans are here, because the light or radio waves haven’t reached them. They would assume this a dead planet. Humans have existed on this planet, in terms of a 24 hour clock, 1 minute and 17 seconds. In terms of exploring space, for less than 1 second.

You see, just because humans have been on Earth about 200,000 years doesn’t mean humans have been emitting radio waves and exploring space for all that time. In fact, we only began exploring space 60 years ago and emitting radio waves for a couple of hundred years. In the history of Earth, we have explored space (in terms of a 24 hour clock) for only a flash of a portion of a second.

That’s us. Now let’s look at the stars.

Let’s say there are 100,000 planets with advanced life like humans on them right now.

However, since the galaxy is 200,000 light years across, someone on a planet on the other side of the galaxy from us would not be visible to us. We’d see that as a planet with no human-like people because it would take light and radio waves 200,000 years to reach us. Now take into consideration that of the 100,000 planets with human-like people on them (as you suggest in your question), it took us 200,000 years to get to the point of emitting radio waves and exploring space. Hence, we’re looking for a very narrow window in a planet’s lifespan that intelligent life might be detected. Not only a tiny fraction of the planet’s existence has it had intelligent life, but only a tiny fraction of the time the intelligent life existed there were they able to emit radio waves and explore space, even if all conditions were favorable for that planet to eventually develop intelligent life.

Furthermore, the sky is very big. Looking for exoplanets, we have explored less than 3% of the total sky so far.

Put all of that together and the chance we would have detected other intelligent life is almost nil to date, even though it might still be out there somewhere. The guy below might be the exception.