Monotheistic gods do exist in the American Gods universe.

Christian figures such as Jesus and saints appear in both the novel and the television series. Figures from the Jewish lore appear in the novel, and Neil Gaiman confirmed on his blog that the Abrahamic God does exist - but since he is an omniprescent being unreacheable and unvisible to the regular human, he does not "appear" per se in the story, while still being there all the time. Allah is supposed to exist too, and Mithra is talked about in the novel