Depending on where in the United States you are starting your travel from, there are four possible routes to Alaska according to the navigation mapquest driving directions.
Most Americans will cross into Canada at the Portal or Fortuna border crossings through North Dakota. While West Coast residents enter Canada at Sumas near Vancouver, Mountain Standard Time inhabitants enter Canada through the Sweetgrass or Piegan–Carway borders in Montana.
The only people who don't have this problem are those who reside in Maine, where taking the 4,500-mile Trans-Canada Highway is the most efficient method to reach Alaska. Consider if you really want to do that instead of taking a plane and picking up a rental car when you get there!