To be fairly honest Japan did not have properly an army at this time, but a feudal system in which that large amount of Samurais were conscripted in times of war and gathered under banners. It would be like calling 200k knights for a crusade, in terms of organization and logistics.
But as said, they could arrive in waves and use the trains to move to more populated areas able to absorb their impact in the economy, and sustain them.
Transcontinental railroad wasn't even begun until 1863.
