Science CAN necessarily explain the big bang because it's a part of science.
Science exists beyond human knowledge. For example, in mathematics there may be conjectures which we may never prove but nevertheless either can or can't be proven.
Math and science are man-made tools to explain what already is. Since every effect must have a cause, so then must everything have an explanation.
Our science can explain the events of the big bang. It may not be able to explain its origins (the pre-universe) but I believe if it can't, then another science with its own physical laws can.