Many authors have written stories about what might happen if mankind's first contact with the rest of the galaxy was with a race other than the Turians. Most choose the Quarians or the Asari. Others have said that mankind would find the Prothean archives before the 22nd century, and be more advanced than in the games. I quite like that idea.
What if they found the ruins earlier, and were more pragmatic about the find, and then made first contact with the Yahg?
What would meeting such a violent and brutal race do to the way humans think and act? Based on my own understanding of the question, I think it would result in a society similar to the Imperium of Man from WH40K. A bulwark against the barbarian, cannibalistic hordes that can only be stopped by lethal force. Their leaders would be ruthless and cunning (think Twyin or Tyrion Lannister), their soldiers equipped with the finest weapons, and their people inured to the horrors of war.
So, here are the specifics of the challenge/plot bunny:
Required:
-Humanity finds the Prothean outpost on Mars before 2060
-Humanity expands peacefully for 10-50 years (long enough for a Systems Alliance-style mentality to become popular)
-First Contact is made with the Yahg, and war erupts
-The Systems Alliance changes drastically to cope with the war
-Human technology becomes better than it was in the war and mankind focuses their efforts on building a massive and dangerous military
-The war with the Yahg ends in human victory less than twenty years before the events at Shanxi/Relay 314 or has been in a stalemate for ten years. If you choose victory, the humans must exterminate the Yahg in their sector of the galaxy
Recommended:
-A human team finds a late-Reaper War-era Prothean database in the interstellar void and brings back schematics for denser Mass Effect cores, particle weapons, advanced biotic implants, and other technology
-Humans develop non-Mass Effect-standard technologies (e.g. laser/plasma weapons ala X-COM, battle droids ala Star Wars, etc.
-Humans have few natural biotics, but they are as powerful as Krogan Battlemasters. Most human armor suits have Element Zero nodes to allow low-level biotics to all soldiers (developed as a partial counter to Yahg biotics)
-The Yahg who fight the humans descend from a colony expedition dispatched from the Yahg homeworld after their first contact with the Citadel and before the quarantine was in place
-A human exploration ship finds the Migrant Fleet, and diplomatic relations begin between the two races before the Turians invade Shanxi. Quarians may/may not provide help against the Yahg (depending on when contact is made)
Forbidden:
-Turian victory at Shanxi
-Humans joining the Citadel as an associate (non-Council) race; they either remain independent or become equal to the Turians in both Council seat and permitted number of Dreadnoughts (if the Treaty of Farixen is not tossed out entirely)