If you look at what Paul said to them, and understand something of who those Greeks were as he no doubt did, I think you’ll find he applied more than pagan ideas.
Realize that those of the Areopagus were disciples of the philosophers, the grammarians, and that long before their mentors had struggled against and vanquished a competing class of teachers of wisdom called the Sophists. Now the Sophists had in mind that a person could actually know what it is to be Man, a kind of wisdom they called Sophia.
One of the protest that the philosophers raised against men being able to know for sure what it was to be Man was sensibly the perceived difficulty that any man, still alive, could know for sure if the soul of man was immortal or not. Now, don’t get me wrong: men like Socrates did make arguments as to why it was reasonable to believe that the soul was immortal but that isn’t actually knowing that it is, and if you don’t know that how could you claim that you knew Sophia?
They simply resigned themselves that there would be, or could be, no compelling or binding evidence on this side of the veil to say that souls do endure.
But Paul preached to them the resurrection of the dead, not just mere resuscitation, which is precisely the evidence they thought they’d never hear!
So what could they do? Well, some mocked ... maybe something along the line of “Hey, we’ve got an actual Sophist here!” ... but others were interested to hear more about this new evidence.
Yes, certain additional information was needed to bridge the gap. But what I mean is that Paul respected the approach that had been made. The bridging information was given as “I declare to you.” It was an assertion of faith. But he didn’t do that with what they already knew.