It means, if we are alone in the Universe, it only means we are the first. The Universe is far from being finished.
That seems illogical to me. Given the vastness of the universe, the odds of intelligent life randomly appearing only once is infinitesimal. If we are indeed unique, there must have been some purpose for our existence.
Given the vastness of the universe there could be millions of intelligent species that we will never be able to detect. So while you may think we are unique, it would just be a matter of faith to actually believe that we are unique- just as it would be a matter of faith to declare that we are not unique.