We know a lot about cosmology. In particular there is very good evidence for for the basic model: hot big bang, cold dark matter, accelerating expansion, geometrically flat, ~14 billions years old (see http://www.astro.ucla.edu/~wright/cosmology_faq.html for more).
Granted we don't know what the dark matter is, and we don't know what's causing the acceleration. Those are big unknowns! But the basic picture is pretty well understood. And I think it's very unlikely that much of this picture is "deeply wrong".
I mean, what do you think? Some day we are going to discover that the universe wasn't really denser and hotter in the past? That the universe isn't really expanding? That baryonic matter makes up all of the mass of the universe?