The million year perspective is what is needed to grok the difficulties in the paradox.
Think of where humanity will be in a million years. If someone thinks that we won’t have an interstellar presence and a civilization detectable from far, far away, then they need to explain why. If they don’t think that alien civs would develop that way, and follow a similar path, they need to explain why humanity is unique in that it will.
There tend to be a lot of assertions that it would require the entire output of a civilization in order to start this process, but nothing could be further from the truth. If we build a single self contained asteroid colony, then that’s all that is needed to continue that propagation across the entire reachable universe. It would not require the civ to gather its resources to send a ship halfway across the galaxy to a particular star, it would just be the colony growing up until some elements of it find another rock to start living on. Rinse and repeat for a few millions years, and you’ve colonized a good chunk of the galaxy without even trying.
And if we are not into colonization, then we would still want resources. If we build an automated asteroid mining operation that can replicate itself, something that is an engineering challenge, to be sure, but not in any way a physical impossibility, why would we not send them further and further out to gather more and more resources for our use?