Well... not sure if you count crossover first contacts as first contact scenarios or not..
Robotech/battlestar galactica cross/contact AA thread
BSG-AA 'Humanity's Survivors' by Multiple - [Dld Date=04/29/2005] - [Dld Size=58kb] - [Dld File Cnt=7] - [Dld Status=Inactive]
- - [Direct URL] http://addventure.bast-enterprises.de/frecent.php?tag=Humanity%27s+Survivors
There was a Ranma/Mass Effect crossover where Ranma met the Asari before they met humanity.
RANMA-ME 'The Human Asari' by Raven In Twilight - [Dld Date=04/13/2013] - [Dld Size=30kb] - [Dld File Cnt=2] - [Dld Status=Inactive]
- - [MD Source=FF.NET] - [MD Rating=T] - [MD Word Cnt=5468]
- - [MD Summary= After loosing everything he loves to a fully powered saffron Ranma ends up being moved to the Mass Effect universe by way of Yggdrasil and the Asgard. How will the gender changing Martial Artist adapt and thrive in this new universe. Beginning of the ME material will be set well before the Mass effect games.]
- - [Direct URL] https://www.fanfiction.net/s/9192941/1/
- - [Author1 URL] https://www.fanfiction.net/u/1133330/
Ranma made first contact with some aliens in the following (additional chapters on TFF in preview):
RANMA-SGSG1 'Scourge of the Goa'uld' by Ice-Tea-1983 - [Dld Date=06/11/2012] - [Dld Size=108kb] - [Dld File Cnt=5] - [Dld Status=Inactive - Preview]
- - [MD Source=FF.NET] - [MD Rating=M] - [MD Word Cnt=19162]
- - [MD Summary= On Second Lieutenant Ranma's first Offworld mission something goes monumentally wrong. Is the universe prepared for the consequences? Stargate SG1 crossover with a few extra special appearances.]
- - [Preview URL] http://thefanfictionforum.net/showthread.php?tid=9044
- - [Direct URL] https://www.fanfiction.net/s/4677821/1/
- - [Author1 URL] https://www.fanfiction.net/u/386101/
A Babylon 5/Wing commander first contact scenario
B5-WC 'A strange twist of fate' by Lucas43 - [Dld Date=08/12/2014] - [Dld Size=877kb] - [Dld File Cnt=69] - [Dld Status=In Progress]
- - [MD Source=FF.NET] - [MD Rating=T] - [MD Word Cnt=164266]
- - [MD Summary= A Confed battle group is trying to destroy a strange ship. And when it does the people of the battle group find out how fickle the fates can be.]
- - [Direct URL] https://www.fanfiction.net/s/2397863/1/
- - [Author1 URL] https://www.fanfiction.net/u/766514/
A author by name of USSExplorer actually has two spinoffs of one of his stories that have first contact scenarios in differing unuiverses. The root story was called 'Vanguard Over Green Fields and Drones'
ST-B5 'Vanguard Settling In' by USSExplorer - [Dld Date=09/02/2012] - [Dld Size=76kb] - [Dld File Cnt=10] - [Dld Status=Inactive]
- - [MD Source=FF.NET] - [MD Rating=K] - [MD Word Cnt=13763]
- - [MD Summary= After the battle the surviving crew of the Vanguard try to work out where they are and how to get home. A slow build crossover. Not going to have much interaction with B5 early on as expand on the Vanguard and her crew.]
- - [Direct URL] https://www.fanfiction.net/s/7959584/1/
- - [Author1 URL] https://www.fanfiction.net/u/280578/
ST-ME 'Vanguard In at the Deep End' by USSExplorer - [Dld Date=02/03/2015] - [Dld Size=1193kb] - [Dld File Cnt=46] - [Dld Status=In Progress]
- - [MD Source=FF.NET] - [MD Rating=M] - [MD Word Cnt=215593]
- - [MD Summary= The Vanguard finds itself flung into another galaxy that faces the threat of being overrun by a seemingly unstoppable force. With a massively damaged ship and little time; can the Vanguard make a difference in determining the fate of a galaxy?]
- - [Direct URL] https://www.fanfiction.net/s/8062951/1/
- - [Author1 URL] https://www.fanfiction.net/u/280578/
A forced Star Trek TNG and firefly first contact set up by Q (it has a sequel as well):
ST-FIREFLY 'Lost In The Woods' by Ardwolf - [Dld Date=10/18/2008] - [Dld Size=221kb] - [Dld File Cnt=14] - [Dld Status=Complete]
- - [MD Source=FF.NET] - [MD Rating=M] - [MD Word Cnt=39901]
- - [MD Summary= Captain Picard’s bad day just got a lot worse courtesy of Q. Which is nothing compared to the day Malcolm Reynolds is about to have when River starts babbling about the kindly t’ien lung and his curious bunny rabbit… ST:TNG/Firefly crossover.]
- - [Direct URL] https://www.fanfiction.net/s/4603570/1/
- - [Author1 URL] https://www.fanfiction.net/u/1716738/
Zcenicx made multiple versions of a story called Task force 43 dealing with what eventually in some versions has first contact between Star Trek and Earth Alliance during Mimbari War (the numbering of the stories this way is my internal numbering, not the numbering by that author).
ST-B5 'Task Force 43 v1x' by Zcenicx - [Dld Date=12/02/2007] - [Dld Size=687kb] - [Dld File Cnt=28] - [Dld Status=Inactive - Preview]
- - [Preview URL] http://forums.spacebattles.com/threads/taskforce-43-st-b5-x-over.125183/
ST-B5 'Task Force 43 v2x' by Zcenicx - [Dld Date=01/18/2009] - [Dld Size=1208kb] - [Dld File Cnt=38] - [Dld Status=Inactive - Preview]
- - [MD Rating=T] - [MD Word Cnt=211048]
- - [MD Summary= TF43 is a larger-than-usual-scale crossover between post-Nemesis Star Trek and Babylon 5. There is also direct theft of ideas from other Sci-Fi universes among others Andromeda Stargate nBSG Gundam Mass Effect and Starship Troopers.]
- - [Preview URL] http://forums.spacebattles.com/threads/taskforce-43-story-only.141490/
ST-B5 'Task Force 43 v3x Original' by Zcenicx - [Dld Date=05/02/2011] - [Dld Size=3289kb] - [Dld File Cnt=72] - [Dld Status=Inactive - Preview]
- - [MD Rating=T] - [MD Word Cnt=595228]
- - [MD Summary= TF43 is a larger-than-usual-scale crossover between post-Nemesis Star Trek and Babylon 5. There is also direct theft of ideas from other Sci-Fi universes among others Andromeda Stargate nBSG Gundam Mass Effect and Starship Troopers.]
- - [Preview URL] http://forums.spacebattles.com/threads/task-force-43-v3-rewrite.156005/
ST-B5 'Task Force 43 v3x Revised' by Zcenicx - [Dld Date=11/28/2012] - [Dld Size=3856kb] - [Dld File Cnt=80] - [Dld Status=Inactive - Preview]
- - [MD Rating=T] - [MD Word Cnt=687592]
- - [MD Summary= TF43 is a larger-than-usual-scale crossover between post-Nemesis Star Trek and Babylon 5. There is also direct theft of ideas from other Sci-Fi universes among others Andromeda Stargate nBSG Gundam Mass Effect and Starship Troopers.]
- - [Preview URL] http://forums.spacebattles.com/threads/task-force-43-story-only.156439/
ST-B5 'Task Force 43 v4x Rebirth' by Zcenicx - [Dld Date=11/14/2014] - [Dld Size=2669kb] - [Dld File Cnt=32] - [Dld Status=In Progress - Preview]
- - [Preview URL] http://forums.spacebattles.com/threads/task-force-43-rebirth.288874/
EDIT1: There is a Tenchi story out there with the *setuP8 to a first contact, but it stops at that point. So not much good to you.
A runner up would be a different Tenchi crossover where he returns from the Babylon 5 universe and introduces the tech to the humans... The dark rewrite is on FF.NET, but I prefer the lighter two arc original as originally presented off his old site. note it does have first contact scenarios with races in the home universe.
TM-MULTI 'Back Home' by Warringer - [Dld Date=07/31/2006] - [Dld Size=1532kb] - [Dld File Cnt=61] - [Dld Status=Inactive]
- - [Direct URL] http://old.warringersworks.com/back-home/index.html
- - [Author1 URL] https://www.fanfiction.net/u/212642/
- - [Author2 URL] http://old.warringersworks.com/index.html
EDIT2: Another sort of one occurs to me...
NGE-MULTI 'Evangelion The Death God War' by zidaneace - [Dld Date=11/25/2011] - [Dld Size=560kb] - [Dld File Cnt=9] - [Dld Status=Inactive]
- - [MD Source=FF.NET] - [MD Rating=M] - [MD Word Cnt=106098]
- - [MD Summary= Long after the destruction of Earth in a distant part of the galaxy Earth’s sole surviving human fights against the powers of the Death Gods and his own internal conflict. The scariest thing is he is more like them than he’d like to be!]
- - [Direct URL] https://www.fanfiction.net/s/3583999/1/
- - [Author1 URL] https://www.fanfiction.net/u/1221371/