This idea has been batted around before, but needed more data to back it up. I remember a number of people considering life on deep sea heat plumes and the chemistry involved. They pointed out that those forms could get started even if the Earth is completely iced over as we now know it was for a fair amount of time. The young sun used to be weaker, so a statistical argument is enough to suggest an early, deeper origin or multiple origins.
There was another version I heard long ago. The earliest life may have started deep in the rocks and not right above them in the deep ocean. Water gets into the rocks in a number of ways and the chemistry still works. Think about the true extremophiles and consider the possibilities for an earlier, slower, protected start. Who needs a UV shield or abundant water then? 8)