When Bigger sees the opulence of the Dalton mansion, he realises just how "down and out" his family is. In his attempt to better himself (Here, note the connotation of his name....), Bigger takes some distance between himself and his family. He is deluded into believing that he can somehow penetrate and become a part of the white man's world:
It is the image of Mary in a newsreel that inspired Bigger to take the job so that he might be closer to whites. He decides that by proximity he might learn how they make all their money. The film encourages him to pursue the American dream even though he is already excluded from it.
In a predestined way, Bigger's false aspirations lead to his downfall. By venturing into the white man's world, he becomes increasingly vulnerable to it and finally panics when the pressure is on. He does not intentionally smother Mary to death but only covers her face to keep her quiet. This act is provoked by the "natural" assumption her mother would have made that her daughter was being sexually aggressed. Note that this is Bigger's presumption of a presumption, but in this respect he was probably right.
In a way, Bigger sets his own trap, but he has been conditioned to react defensively, even in the absence of a real threat. The mere dread of facing the supposition of guilt is enough to set off the domino effect of violence, and Bigger's downward spiral thereafter is inevitable.