Not really. We don't have evidence that Father Christmas does not exist.
What we have is evidence that the presents put out for children are, on all investigated occasions, put there by their parents and not by Father Christmas. But he could exist. It is just that there is no evidence for him and so we apply Ockham's Razor and do not invoke his existence to explain what we observe.
Father Christmas is thus an
unnecessary hypothesis to explain the appearance of presents on Christmas Morning.
And, er, God is um, ah, very much in a similar position, I would say, at least from a scientific point of view.