Passage of Earth is a short story by Award-winning (Nebula et al) author Michael Swanwick, published by Clarkesworld.
I cannot really call it a first contact scenario (although it takes place as part of one), as it plays out at the moment when humanity thinks they finally got their hands on a number of alien 'Worms' after one of their spaceships ends up in the Pacific. We see the mortician Hank perform an autopsy on one of the cadavers, brought in by his ex-wife, who now works for the governement.
Now, things are never as simple and straight forward with Aliens, of course, and this story has multiple levels of complications and implications which I won't spoil by pointing them out to you before you read the story yourself. You know the old saying about staring into the void... this here is similar, if a bit more physical. Passage, in ever so many ways.
The story is impressive, with a very interesting twist to it. And whilst I found some of the stylings and plot sub-threads to be over the top I would suggest you make up your own mind, this is inventive stuff right here. The story can be read on the Clarkesworld website for free - links are below and to the right.
The picture on the right is, despite its Alien looks, of an Earth creature - namely a Scale Worm.
Links: Passage of Earth - Michael Swanwick - Clarkesworld - Scale Worms