Maybe a reason that Sabertooth killed his commanding officer in 1973 despite successfully posing as a normal human for over a century was because he finally boiled over in anger about being drafted and deployed to Vietnam despite the Paris Peace Accords (signed on January 27 in real-life and conceivably in the movie as well) already being signed.
As I understand it combat operations went on for two more months in some capacity. So there's a little wiggle room, though probably not much. ( We might also ask why no one in the film appears to be dressed like it's January.

)
He must have. The main story of Origins takes place in 1979 in accordance with the real-life Three Mile Island accident
That's the
main story of Origins, though. That material is preceded by a six-year gap which just so happens to fit neatly in between 1973 and 1979. ( And that's assuming the
Origins Three Mile Island incident must have taken place in the same year as the one in real life. )