Just not necessarily at the same time, or with sufficient resources to reach us.

The idea that an infinite universe means infinitely many advanced civilisations is appealing but I think your statement oversimplifies a complex issue.

Firstly, the universe's infinity is not a settled matter; current cosmology suggests it's vast but finite, but of course, there's no absolute answer to this (yet). I'd also look to the Drake Equation when considering this point, which illustrates the myriad factors and sheer number of uncertainties involved in the development of "advanced civilisations".

So, yeah: while advanced civilisations are certainly possible, they may not be as probable as you suggest, even in a universe brimming with stars and planets.

And if they are outside our light cone, they just as well might not exist. There is no-one and will never be anyone to hear that tree fall in the forest.

Not when you're thinking in terms of probabilities.

I don't understand. If one of the advanced civilizations out there, is so far away, the light emitted from them will never even catch up to and reach Earth, what does it matter that they exist?

Because it'd still help inform us how prevalent life is in the Universe.

We didn't even know how many stars had planets until not so long ago. The idea we're any good at detecting advanced civilisations in the visible universe is highly questionable.

But how easy they are to detect is separate from the Drake equation - it's there only to demonstrate how many uncertainties there are.