The English language M:GAlpha doesn't seem to include any reference to how many years have passed since the red plague, at least not that I can recall or quickly find. But the blurb on the back cover begins, "01/19/2278, 3:47pm." So if this were to be shortly before the campaign begins, I'd set the current year as between 2279 and 2281, depending on how far your zone is from where you place Paradise Valley, (if you've gone into that sort of detail) and how recently animal mutants arrived in the area.
Unless of course you decide to have your animal mutants hail from somewhere else, at which point it hardly matters. Our initial campaign predated Genlab and had two animal tribes: the settlement of Ondo Zo (London Zoo) was run by a lion hybrid, with an elephant chief enforcer; while we never knew the name of the other lot, as things got violent rather quickly there and we just called them mutt-men.
For the sake of completeness, the Mechatron blurb also begins with a time-stamp, this one for the evacuation of humans from Mechatron7 - 10/07/2153, 0617. So we know that the Enclave Wars were in full swing at this time.