Well, it's an assumption, alright...but we have to give its proponents this much credit: that it is based on an observation that strict cause-and-effect seem to work many circumstances, and the extension of that to the speculation that maybe human experience is the same -- so it at least has some empirical precedents from which it can extrapolate. In fairness, we have to give it that.
But I think the situation of the Determinist is even worse than you imply when you say it's an assumption. The person who believes in some measure of free will, or at least in the human volition as a potential causal agent, can argue for her own view, and can also consider the possibility of Determinism, if she wishes; but according to his own creed, the Determinist cannot actually "consider" anything but what he is predetermined to think about. He has no choice about what he happens to believe. "Choice," according to his view, is just the name we give to determined forces we do not happen to understand.
So the person who believes in will can consider two views, and the Determinist cannot actually "consider" anything at all.