It's very safe to say most of what we know about cosmology is wrong, and a large portion of it is probably deeply wrong.
It would be pretty surprising if we're "fundamentally wrong" about cosmology, given that scientists are aware of what goes where, with respect to these categories. Plus, I'd imagine a lot of cosmology is purely observation, anyway, and you can't be "wrong" about observation.
There is a lot of room between "omniscient" (which many people mistakenly demand of science) and "wrong". In other words, science can and must deal with partial knowledge.
Those events took place under conditions of gravity, temperature and pressure that we can't reproduce.
Those theories include belief in a phenomena called inflation which is not predicted by any theory we have in physics today, and which has some internal contradictions. (See http://www.edge.org/q2008/q08_4.html#Steinhardt for an explanation of some of them.)
Oh, and the thing we can look at to test these theories? That's the cosmic background radiation which is believed to have been formed several hundred thousand years later.
Are you still confident in what scientists currently claim about cosmology?
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?
If you've followed cosmological history at all, it's been a cascading series of big changes decade after decade.
I'm virtually certain the model of 2030 will vary in deep, significant ways from the model of 2010.
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.
I do believe that our current understanding of cosmology has hardly scratched the surface of describing how things really are. However, any future model is not going to invalidate current observations, but rather, better explain them.