The most recent episode "If-then-else" gave the most insightful look yet at how the machine operates. I think of ST:TNG "The Nth Degree" where Barclay tells Laforge, "I can conceive of almost limitless possibilities and think through all of them in a nanosecond."
As humans, we operate at one second per second. The machine, at billions or trillions of operations per second must see humanity as absolutely frozen. Since we cannot hope to speed up, the machine is always waiting for us to do something. I can't help but to think, does god get bored?
A human being on average will have approximately 2.5 billion heartbeats in their lifetime. [Nova online] If you equate this to clock cycles per second, a human lifespan would be less than one second in machine time. The machine then is, for all purposes, immortal.
Coupling immortality with near omniscience, you have to ask: Could the rising of Samaritan not been seen in any of the simulations?
There are two critical times that are pivotal in Samaritans creation. The 'chip' needed to run the AI program and the 'AI program' itself. And to a lesser extent the warehouse full of servers and the generators needed to power them as they are not in and of themselves unique.
As the threat level to the machine rose and Finch became aware of another AI program, every effort should have been made to stop it. UNLESS the machine foresaw its creation and decided the best way was to blind it to the machine gang and deal with it later, ala, better the devil you know.
You can think of endless possibilities as to why the machine did this or that and all logic would be circular. Ultimately if god is bored, the only way to have companionship is another god. After all, Colossus made no warning until Guardian was already running.