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”.