I guess you (
@Vincent Peri and
@Patrick Gisler ) are drifting away from the question. Well, I shouldn't blame you for that as the question itself is wrong as, at the time of the big bang, the universe didn't even have carbon!
So, I am providing a direct answer to your two questions.
First question: Do genetics markers contain carbon as in the Big Bang carbon and is it possible that all the genetic markers in humans go back to the Big Bang?
Ans:- Already stated above, the universe didn't have carbon at the time of big bang. But, it's true that all the genetic markers in humans, in fact, every bit of higgs boson in humans date back to the Big Bang.
Second question: Is all of the cosmos embedded in all of our genetic markers?
Ans: - Now, this question is like asking whether all of nature can be represented by a green plant. A direct answer will be a bold
NO. As one plant can't survive without the ecosystem, one human gene can't contain the code of the universe. It is a part of it. Not it itself.