Is it more likely that the very first living organisms had a linear genome?
It is hard to give an answer to this question that is not just speculation.  We can be reasonably confident that the most recent common ancestor of bacteria and archaea had circular genomes.  However, we currently have no way to get any conclusive evidence earlier than that.  3 billion year old DNA doesn't fossilize.  So it's just speculation what DNA looked like back then.

On the other hand, my understanding is that most experts think that RNA genomes predated DNA genomes.  These RNA genomes would be linear.