White can force mate from any position.
As an example, put the white queen on a1 and the black king on h8, as far away from mate as possible. White plays Qa8+ and black must move to the seventh rank. Say he moves Kg7. White can move Qe8. If black moves to the sixth rank, white can move the queen to the seventh. By repeatedly trapping the black king to the edge of the board, he can force the black king to the first rank. With black trapped to g1/h1, white can move to e2, then to g4 and (if necessary) h4 to get on the far side of the king. More of the same will force the king back to the first rank, where the queen can chase it to b1 or c1 and deliver mate.