We find in Romans 1 and 2 a couple of interesting things.
One, the awareness of creation should lead them to conclude that there is a Creator.
Two--an awareness of law. That is, of right and wrong. Paul says they are a law unto themselves.
So each person has a moral code of some kind (the law written on their hearts?). Their problem is that they can't keep it perfectly. That will be the basis of their condemnation.
In the same way we we understand that the Law condemns us (the schoolmaster), their own law condemns them. For those of us who have heard the gospel of Jesus Christ, we recognize that conviction is of our sin (breaking the law) and God's righteousness (which we lack).
The heart of the gospel is that Jesus died for us, so that we would not have to bear the punishment for breaking the law.
Since the pagans have no such gospel, they can't be condemned for rejecting Christ. Their own moral law condemns them.