The big bang theory 13.8 billion years ago is just that, a theory.
I don`t know how old the universe is and I don`t know how old the earth is but by reading the creation story I get the idea God did have a plan for evolution which Adam was not a part of.
Adam came along much later in a special creation, that is why we know about how old he would be.
Yeah Adam came later ... I count FIVE DAYS LATER ... :-) ...
Adam came along on the sixth day, measured by evenings and mornings.