I was reading about CMB after this new breakthrough last week and I could not figure this out. The CMB did not exist before the epoch of Last Scattering. They were just photons which were formed at the Big Bang and were travelling in a straight line. If this is true, why is it that the CMB gives us information about the nature of the Universe just after the Big Bang and not the Last Scattering? Even if the origin of these photons is the Big Bang, the scattering should have completely changed their properties. How does it still tell us about the Big Bang?
Well, the argument is something like this.
Matter and radiation are tightly coupled until the time of last scattering. The photons are in thermal equilibrium with the plasma surrounding them. This means the state of the Universe at the time of last scattering is very precisely imprinted on the photons, and the photons travel from last scattering to us more or less unchanged, except for being redshifted by the expansion of space (and a large number of smaller corrections).
At the time of last scattering, and at earlier times, the Universe was in what we call the "linear regime". This means the evolution of the state of the Universe (e.g. the density at each point, temperature at each point, pressure, bulk velocity, etc.) is well described by linear approximations to the usual non-linear equations. Linear equations can be solved exactly, so if you know the state of the Universe at one time in the linear regime, you can easily solve for the state at another time in the linear regime. Broadly speaking, if you look at any quantity evolving in the linear regime, how it is distributed does not change, only the amplitude of fluctuations in the distribution does.
If we think the CMB accurately tells us the state of the Universe at last scattering (at the very least, it gives us a LOT of information about this state!), and that the Universe was in the linear regime at the time of last scattering, then the CMB accurately tells us about all earlier times up to the end of inflation (not to be confused with the expansion of the Universe), in other words all the way back to shortly after the Big Bang.