Paul had been raised as a Jew and had lived among Jews. So, A god not made by human hands would have been a basic, long-accepted truth for him--but not so for the Athenians. As would the existence of God not lots of gods.
Paul is talking to people who would not have been brought up on the Scriptures that had formed and nurtured his understanding.
They may not have known about God, but God knows about them. "We are God's offspring," he tells them. It's hard for some of us to go this far. Although like Paul, we may believe that God created them since God created everything, we still aren't quite ready to accept that non-Christians are also God's children.
Paul then talks about the future, what is necessary for them and for all of us to do--Repent. We might be able to plead ignorance if we really had not been told something, but once we have been told, ignorance is no longer a valid excuse or even explanation. Paul tells them, "The day is coming when God will appoint a man to judge the world in righteousness."
What we do does matter. We will be judged. And since we will be judged righteously, that's the way we should be behaving.
"You can be assured of this," Paul tells them, "because he has raised this judge from the dead."