There are at least three versions of a monotheistic god that I think would make logical sense:
The Hallmark friend
This god did not create the world, with all its devastating natural disasters. She did not create human beings with their tendency to hurt one another. And she has no power to stop all of this evil from happening. What she can do, though, is comfort people through troubled times. She can feel people’s pain, and she loves everyone. (This is my favorite of the three.)
This god created the earth and humans, but hid himself and made it look as if everything came into being naturally. He is driven by pure curiosity: he just wants to see what happens. He could intervene to stop our suffering if he wanted to, but he just doesn’t care that much. Besides, it would spoil the experiment.
The mediocre general
This god created both the earth and humans, but the evil of natural disasters and human sin caught him completely by surprise. To make it worse, his time is occupied with a never-ending battle against Satan, who delights in evil and wishes it (evil) to continue. The match is fairly even, but Satan’s long string of victories indicates that he may have the upper hand. It’s not clear whether the mediocre general will eventually be able to snatch victory from the trident of defeat.
It’s too bad the most popular gods these days are mash-ups of the above three gods – it makes them far less convincing!