I was told that ancient Greece never contributed anything original to math and science
that Babylonians and Egyptians already knew many of the greek concepts
The first sentence doesn't follow from the second one.
On maths that's plainly and utterly wrong. It's true that Egyptians, Babylonians etc. knew some of the things that the Greeks knew, like the Pythagoras' theorem. However, they had no proofs for these things. Greeks came up with the method of mathematics: taking some things as axioms and deducing the rest from them. That wasn't only the foundation of maths, but also an ideal to which all the science and knowing aimed at for the two following millennia, check Descartes and Spinoza for an example. Someone could say that this ideal even slowed down the scientific progress, but that's another topic.
It's a different thing to think something is true and to
know it because you have justification.
Aside to that, Greeks also knew a great deal more than their predecessors, whose knowledge was mostly just arithmetics. Instead of listing all of it, let's just remember that Arkhimedes came up with the basic idea of the integral calculus, and came very close to give it the rigour it achieved not until the 19th century.
Actual sciences is a different thing. Like Hobbsyoyo said before, they didn't really have the method for science then (maths isn't included as science, as it has different method, i.e. it doesn't rely on observation). Aristotle's physics based more on everyday observation and speculation than systematic inquiry. There was reasons for this too, first they didn't have good measuring tools, and foremost, they were in trouble with unreliable observation. They knew very well that you can't always trust your senses, and they had Zeno's paradoxes that were troublesome when you try to even start making a mathematical model of the physical world. Since maths had been so successful, they thought physics should follow the same method too. I'd think it's fair to say that the empirical method had to have a similar triumph (Newton) before it became accepted as the method of physics.
Of course though, Greeks still made progress in physics too. For example, they came up with the sizes and distances of the Moon, Earth and Sun via observation, and some of them based the heliocentric world view on that. What's different from mature physics is that those were more of single facts without a theory to explain them all. So, you could say that the ancient Greek physics is related to the modern in the similar way that the Baylonian or Egyptian maths was related to the ancient Greek maths.
As to what your friend has told to you, I'd think it's just the way people use to speak. It's uncolourful to say things like "The Greeks made use of the knowledge of other civilizations to further the knowledge". It's more fun to say something more flamboyant. Some people may do that to appear smarter. That's what hoaxters rely on too: if you say things confidently enough, people don't require evidence, they are satisfied to be as sure and look like as smart as the guy who says: "Actually, X was overrated, almost everything he did was already done by Y".
Disclaimer: don't trust me on the physics part. Do trust me on the maths.