I think the first few seasons of Babylon 5 is a better analogy. In fact, the first few seasons of Babylon 5 is basically about the struggle between the older races and the younger races. It's possible that we are one of the "old ones" but an early stage. It's also possible that we are one of the younger races but, to the "old ones" we are nearly indistinguishable from ants (G'Kar gives a nice speech about this).
On a more serious note, anyone who has sat and given some thought to what the TFS talks about has probably realized that we could be one of the earliest sentient races. The universe didn't start with the ingredients of life. It was brewed in stars and then spread by the exploding of stars and the re-coalescence of that material. That shortens the possible time frame for sentient life but, you also need a fairly quiescent part of the galaxy to give sentient life enough time to form. So, really, it's impractical for sentient life to arise until *all* nearby giant stars have gone supernova. Then you have the time it takes for new solar systems to form and stabilize, basic life to come into existence, mass extinctions, the possibility that lifeforms unsuitable for sentience will dominate a planet, etc, etc.
It really takes an extraordinary amount of luck, over an extraordinary amount of time, for sentient life to form. And, as we've seen in the last century, it also takes a lot of luck for a technological society to not destroy itself.