KALININGRAD, Russia—Military maneuvering here in the Baltic region by Russia and NATO presents a challenge for President-elect Donald Trump and his commitment to America’s European allies.

The North Atlantic Treaty Organization plans to station a multinational force on its eastern flank by May as a deterrent following Moscow’s aggression in Ukraine. But already in January, a brigade from the U.S. Army 4th Infantry Division will arrive in Germany and then move to Poland—before Inauguration Day, according to U.S. military officials....