It is a lot easier to document that the Greeks had cutting-edge engineering than to prove that it was based on theoretical knowledge.

Greek aqueducts and post-Greek Roman aqueducts were much better than pre-Greek Roman aqueducts. The process of building them may not have been better, but the choice of what to build was more sophisticated. Before the Greeks they just had water run downhill, requiring tunnels and bridges, afterwards they also ran water uphill. So the Romans definitely learned something from the Greeks. Some people think that they must have understood something about water pressure to do this, which would count as science. But there is no record of how they did it, neither theory, nor rules of thumb developed by trial and error. It is a great mystery that the surviving books by Roman aqueduct engineers don't seem adequate for running the aqueducts, let alone building them.

(By "the Greeks" I mean the Hellenistic period of 300-150BC.)

A better documented connection between theory and application is that Archimedes wrote a book on the theory of simple machines and invented the screw pump. However, that history is also controversial.