As I understand it, there's a barrier to seeing beyond approximately 1/1000000th of a second after the big bang, due to total saturation. That's what cosmic background is.
Not quite. The barrier to our ability to see is indeed the Cosmic Microwave Background, but that is from when the universe was about 300k years old, not less than a second. What the CMBR is, is a remnant of the era of recombination, ie when the universe had cooled enough to allow electrons to bind to atomic nuclei, thus making the universe no longer opaque to light. (Previously it was a hot and opaque plasma). So when you look at the CMBR, you see the light that had been previously getting bounced around within that plasma, finally getting freed once atoms formed.
It might help to consider a similar example of this, which is sunlight. The photons of sunlight had been created deep in the core of the sun, but it took those photons a very long time to reach the surface, getting absorbed and re-emitted trillions of times in the process. So when you look at the sun, you don't see all the way to the core, but you see to the depth at which the plasma density is great enough to be opaque to light.
Any evidence of previous whatevers (or concurrent ones, which seem more likely to leave a mark) would have to be behind that barrier, and the cosmic background, because it's expanding and the marks would be left on the outside of the bubble.
The evidence they're looking at here is imprinted on the CMBR itself. What it is is the signature of fine structure that appears to have been created before the Big Bang happened. Specifically, huge rings around galaxy clusters that appear to be shockwaves from pre-Big-Bang-era black holes merging together. Seems very far-fetched to me but the evidence is right there. What matters is how we interpret it, and I'm not 100% sold on this interpretation. Those big rings might very well have been caused by something else we don't quite understand yet. Obviously, more research required.
