The problem with saying 'there is no extraterrestrial life because we haven't observed it and it would probably be here by now' is that there is always the first wave of lifeforms who would come to the same conclusion.

You could make a good case that we are part of this first wave: -The stars created after the big bang would not have had any heavy elements and therefore wouldn't have had the resources to create life. -These stars lasted ~10Bn years before they started to go nova (which creates the heavy elements for the next generation of stars) -Based on our experience, it takes ~4bn years for life to evolve in a planetary system. -Therefore the first lifeforms wouldn't appear until roughly 14bn years after the big bang. -The universe is currently 14bn years old.