I could be mistaken but I believe the hypothesis is that at one point the universe had an average temperature and matter distribution (pressure) to make it so that in most or at least a large portion of the universe it was significantly easier for organic molecules to start forming including the building blocks of DNA and then when it cooled/expanded some of that organic matter made its way to earth to eventually turn into life.
I could be mistaken but I believe the hypothesis is that at one point the universe had an average temperature and matter distribution (pressure) to make it so that in most or at least a large portion of the universe it was significantly easier for organic molecules to start forming including the building blocks of DNA and then when it cooled/expanded some of that organic matter made its way to earth to eventually turn into life.