As far as I know you have an unlimited amount of time. The alien difficulty ramps up somewhere towards the end of the first year I think when Ethereals show up (don't quote me, I can't remember exactly when they first appear).
However, game difficulty plummets as you develop power/flying suits, strong psi soldiers, soldiers with way better stats, and an endless supply of cash. So depending on the rate of your research and progress, it might get a bit harder, but then can do a quick turn around and get too easy.