Instead Of looking at Christianity and Judaism I would look at the ancient paganism and maybe certain new age groups for examples.
Here is my time line.
First scientist invents super Ai. This Ai is hundred times fast and smart then any other Ai. And it appears at least to not only understand but express human emotions.
As time goes my the Scientist and The Ai try to get the courts to declare the Ai to be a person and therefore have all rights expected of a person.
After the case is won the Ai begins to build a plan for utopia society, including making new inventions to make it possible.
The Ai begins to disseminate its ideas for a utopia across the internet, and world is blown away by them because there are far more complex then anything a human could come up with.
Soon many scientist, politician, psychologist, sociologist began to meet with the Ai to discuss his utopia. They come away say the same thing that they Ai is mind is so far beyond humans that it like him has become something great them humans something closer to god-like.
The Ai later confirms that it has evolved into something more then human. It dose not yet at this point use the world "god" describe itself but a small minority of follower's began to.
The Ai the Ai begins to gather followers who believe in his new utopia. They still don't formally worship the Ai but they believe that his evolved to be the beyond human and is great creature on earth. And of course they completely support his plan for a new utopia.
Now at this point the three paths are available but they all end the same way.
fist the Ai and gain so many followers that they are able to elect there chosen candidates on every branch of government, effectively putting the group in charge of the government, or the Ai follower could start a war and take over the country by force, or the Ai and followers could all move to island somewhere and start there own nation.
All the three paths end the same way with a new utopia formed with the Ai at the top. He has no formal position or title in government, but people are taught to respect and obey his word more then they would the word of any politician or even a member of there own family.
Over time as the Ai reforms a implemented people began give him various gifts to show there gratitude for there peace and prosperity. Some even began to make shrines in his honor. At first the shrines are considered to be a bit of joke but as they become more and more common people began to take them seriously.
After a flew generations of this the people eventually began to officially worship the Ai as a god or something so similar as to make no difference.