You can say, "In the freezer my mother keeps a lot of ice cream. Nothing else can fit." As two separate thoughts, that's fine. But if you want to connect the two sentences with "that" then you would replace "a lot of" with "so much." When you say, "There's so much (...)" like "There's so much ice cream," the use of the term "so much" implies that there is a consequence to there being so much. When you add "...that nothing else can fit inside," then your explicitly saying that the fact that nothing else can fit inside is a consequence of there being so much ice cream.