I am sure there were times when GI's tried to carry as much ammo as they could, but generally, infantry likes to travel light.* I don't know of any action in which there was a shortage of ammo, but if there was there were always some of your side's soldiers who didn't need theirs any more.
I suggest a trip to a good library and a look at the WWII Time-Life picture books, as well as the "Willy and Joe" cartoon series. Don't trust re-enactors or even folks who were there, since memories fade.
*Which is why those stories about how "my uncle left me six German Mausers that he captured and carried with him until he came back...." are unlikely to be true.