It's a World War II scenario for active military personnel advancing into heart of Germany. Mission after mission were assigned without wasting much time. And whatever time they had they rested, took bath and ate.
In the movie Fury, there doesn't seem to be a point that the soldiers rest and sleep.
In the opening scene when team "Fury" arrives at base being only survivors of their platoon many soldiers are seen mobilizing, managing PoWs and some are taking rest. You can also see a signboard "Shower Unit".
In another scene when Collier meets with Captain Waggoner where his unit is waiting to be mobilized. That's pretty much rest for soldiers then.
When Collier succeed in taking up the town we can see soldiers having leisure time.
From Elison's point of view
As for the movie we see that Elison joins and probably within 1-2 days crew of Fury is killed in battle. I say this because there is not much time passed between his joining, learning the bitter truth of war (brutal killings), falling in love and becoming "Machine". As he is not shown being aged or spent too much time with crew.
In conversation with Captain Waggoner
Wardaddy: What am I walking into?
Waggoner: A recon plane spotted a troop concentration moving west, here. (pointing towards map)
Earlier when Fury and other teams headed to join Waggoner we saw 4 recon planes flying right past them.
So my guess is they provided the intel the next day about approaching German regiment.