You're both correct. We know a lot about cosmology compared to what we knew, say, 100 or especially 200 years ago. Many of the big, open cosmological questions throughout human history (what is the Universe, how was it created, how old is it, what are the stars, what powers the stars, how far away are galaxies, etc, etc) have been answered.

We should not downplay that remarkable achievement. We know the age of the Universe to high precision, despite the fact that that age is fully 6 orders of magnitude greater than all of human history.

Nevertheless, there is still much we don't know, and likely what we don't know easily exceeds what we do know, by a fair margin. We do not know the nature of the majority of dark matter, we do not know the nature of "dark energy", we do not fully understand why the Universe is filled with matter rather than just energy, etc.