Historically, the Soviets in particular were quite good at rapid bridging operations. The Germans had rollbahn repair troops who kept roads and railroads open. The railroad bridges were not necessarily intact when captured and in fact not necessarily replaced during the war - cargoes would often be unloaded, taken across the river on temporary bridges, and then loaded on trains on the other side. This continued to be the case in Europe well into the late 1940's - my parents remember a trip from Cherbourg to Bordeaux in late 1945 that involved "innumerable" river crossings at broken bridges across temporary structures and took six days (for a journey you could do today on the autoroute or in a train in four or five hours).
The game abstracts this by, for one thing, making rail journeys take far longer than they would in peacetime. It certainly wouldn't take more than a week to travel from eastern Germany to the Volga in 1938, assuming you had the proper passports. Another abstraction is the cost in MP for crossing a river during normal land movement, which again can take almost a week for a major river if you are crossing into an enemy zone of control. It goes more quickly if your side controls both sides, but still can take a significant fraction of your weekly allowance of MP, reflecting the time needed to go up or downriver to find an intact bridge or to build or repair a bridge where you want to cross.