Part of this is inference on Claudia's behalf. She was exceptionally clever to figure it out. It wasn't easy to figure this out and the evidence is few and far between.
However, it's important to realize that the knotted worlds were created after Tannhaus' family died, since origin-Tannhaus does so after Marek, Sonja and Charlotte were killed).
That means that both Adam-Tannhaus and Eva-Tannhaus have also lost their family.
The same applies to essentially everything that happened in the Origin world before Tannhaus created the knot.
When you compare Adam and Eve's worlds, some things match and some things don't.
- The things that don't match all originate from the Unknown in some way.
- The things that do match are facts that carried over from the Origin world.
You can start making a few educated guesses here. If both Adam-Tannhaus and Eve-Tannhaus lost their family and delved deep into the idea of time travel, then Origin-Tannhaus is likely to have done the same. Especially if you find out that he was already into it before his family got killed (since Marek himself throws it in his face in the series finale).
We don't know Claudia's full thought proces. We just see her explain what she already knows to Adam, she doesn't explain how she found it out.
But given the cyclical nature of events, and the bootstrapping done by (old) Claudia constantly transferring her complete knowledge to (middle age) Claudia, that means that Claudia essentially had an infinite amount of time to expand her knowledge and figure it out.
Every cycle's Claudia has 33 years of knowledge to pass to the 33-years-younger Claudia, who then in turn passes that acquired knowledge + her own 33 years of knowledge down to the next Claudia, and so on.
We have no way of knowing how many cycles there have been. It could have been millions, billions, trillions, ...
It's reasonable to assume that Claudia would at some point have a theory. Maybe she had thousands or millions of other theories that never panned out.
We only get to see the theory that turns out to be correct.