Who's contact? The Drengin had enslaved the Torians before the humans made contact with anyone. The Iconians created the Yor. I can only think of one event that happened simultaneously for all races. The game should start at 0AH. "After Hyperdrive" Or Post Hyperdrive, or 2AH if you want to count from the time the humans sent the hyperdrive schematics, or whatever. This is probably the same timeframe that you were thinking of, but I think this would be a more precise term for it, given the imprecise nature of first contact I just mentioned.
Not only is that the most major thing to happen to most of the races in recent times, it's the only thing that lines up with all the other races. It's the start of a whole new era, much like the discovery of atomic energy. While I don't think that AE (Atomic Era) numbering will overtake the use of AD any time soon, that's an indication of the kinds of things that societies will set their clocks by. Most fleshed out SF that I've read base their years on years since man left Earth, or a more recent major event (founding or fall of a major empire, etc).
We can argue that not all the races would be using the same definition of a year, but since we were all in contact with one another electronically it seems (otherwise, how did the humans give everyone the hyperdrive?), we may have found time to agree on what a galactic year is for inter-species communication purposes. Or, you could just use a floating point number for the time and each race has a fixed floating point multiplier in the 0.5-2.0 range that modifies it. Of course, that means that one race's 10AH could be another races 40AH. Floating point years or stardates or whatever you want to call them would also avoid the idea that all races break down a year into 12 divisions with 4 subdivisions within each division.
In the end, though, you have to admit that this is a minor asthetic issue.
On the other hand, if you go with 50 "weeks" per stardate "year", you never need more than 2 digits after the decimal point, making them look a little less awkward. It also gets us out of the trap of "We did WHAT in 161 hours total!?!?" The week/year is no longer defined in terms of anything we can measure against, so we don't have a frame of reference for how long it took to do something.