It probably wouldn't have been challenging to land a force to occupy a part of Alaska in 1928 because it was lightly defended and has so much coastline, the problem is ensuring they don't die of frostbite or starvation afterwards. That's extremely difficult since even without the US Navy (which is far greater than the Soviet Navy in numbers and quality), the sea conditions are terrible most of the year. Gales are common and can appear without warning. Go watch Deadliest Catch, that's what your resupply would be dealing with. Worse, many areas in the Aleutians and Gulf of Alaska coast have extreme tidal variations (Cook Inlet, which Anchorage lays on, has tides almost on the level of the Bay of Fundy) and strong currents which can wreck ships or drive them off course.
There's also the problem with how easy it is to mine the coast. Look at the narrow channels around Juneau or Sitka or even Anchorage. It's very similar to Norway where a small fleet of minelayers and torpedo boats punches far above its weight. And those three cities are practically the only cities of note in Alaska in 1928.
Only Britain or Japan could probably invade Alaska in that era, and if war looked likely with either than we'd see a lot more fortification in Alaska, local recruitment, etc. like happened in the 30s/early 40s.