What do you mean liquid water in space? Liquid water doesn’t exist at low pressures, so you also need a somewhat pressurized environment like an atmosphere
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 don’t see how this could work, DNA degrades fairly quickly.
For those conditions you’re looking at a hilariously long time in the past, presumably closer to the big bang than now, and DNA can’t even last 100 million years.
Granted it probably lasts longer if frozen, but it’s not like things just stay frozen forever, and when we’re talking about thousands and thousands and thousands of years it seems incredibly difficult to believe that life would have started that way, especially compared to the relatively easy to imagine “water built up on an almost-molten earth, minerals leeched into it, and the heat caused chemical reactions that eventually ended up forming RNA or something”.