While I agree that ME1 did very well in setting up a new sci-fi universe that seemed different from the norm (the norm being one where humans are already either the most dominant race in the galaxy, or at least one of the most dominant), there were hints of human exceptionalism even there. All throughout the game we encounter aliens talking about how quickly humans have embraced mass effect technology, how quickly they've spread out and how powerful they've already become in just the 30+ years since they even discovered the mass relays. (Don't get me started on that last bit, by the way; I think humans becoming so big and bad in thirty years
is freaking ridiculous.)
Then they talk about how it normally takes centuries for a species to build up enough power and influence to earn a seat on the Council, yet humanity has earned one by the end of ME1. Again, far faster than any other species has ever done so before.
The Humans Are Special trope didn't start to become really blatant until ME2 and especially ME3, but the seeds of it were already present in ME1.