This is a difficult question to answer because George strikes me as being fairly consistent from beginning to end. If, however, there is a moment of change or development for George, I would identify two possible critical moments for this development.
The first moment comes when Carlson convinces Candy to allow him to shoot Candy's smelly old dog. Eventually, George will have to make a similar decision about Lennie, after it becomes clear to George that Lennie will become the victim of a lynch mob. George's witnessing of the events involving Candy's old dog teaches George that ultimately he will have to make the same choice.
A second critical moment of possible growth for George comes when Candy expresses interest in the farm of which George and Lennie dream. When Candy indicates that he is willing to put up his savings to help finance the purchase of this farm, George suddenly seems to think that there will actually be a chance of accomplishing their dream. Thus, Steinbeck writes, "This thing they had never really believed in was coming true." Such a comment suggests that perhaps for the first time George does believe in the utopia that he has been using for years to pacify Lennie.