that human brain processes most information subconsciousely (it is fast thus more efficient), - exactly the same way as a brain of all other animals does. You may call it intuitive or instinctive processing.
Just a few facts about subconsious processing of important tinformation (without engaging neurons responsible with speach or images).
It was important for survival to identify predator hiding nearby. So, during evolution any ability to gather information about predator presence and then prompt processing of this information to make vital reaction was extremely important. It helped to survive (and pass to offspring the ability to recognize danger quickly).
So, any bit of useful data - new smell, sudden stop of noise (when predator had noticed you and stopped moving or breathing), any periferal vision of motion or of stop of motion, tiny wibration (or sudden stop if it), any periferal vision recognition of pair of stearing eyes, hearing birds stop chirping, etc - not paying attention to this information and not processing it quickly and subconsciousely (the only way animals can) was fatal for survival. Thus such abilities were selected by ruthless predators by eating those who can't notice small changes and process them quickly.
Therefore, when you move in the croud your brain quickly estimates who's trajectory is in collision with you 3-5 seconds down the road and brings your attention to them ignoring others. Then you slow down, or accelerate, or turn to avoid (potentially dangerous) encounter.
Of course, you notice anyone or anything APPROACHING you (as no side motion and rapidly increasing size of object) by periferal vision subconsciousely well before he is near.
Monitoring moving objects is so important for survival that it is the job brain is constantly doing subconsciousely by periferal vision - too dangerous to ignore. So, when it comes to jump out of bus brain knows what is going on around the bus (by memorising what was seen periferally via windows a few seconds ago) and which car you are likely to hit. Unfortunately, often we neglect this information by actively thinking about something else at this moment, and can indeed be hit as a result.
When you read a book and somebody calls you, returning back to reading not only a few minutes, but hours, even days later, you almost always start exactly at the place on the page where you were interrupted - and it is fully subconscious act to return to this site.
When you don't have alarm clock around, you brain itself often wakes you up on time.
When you forgot and are about to miss something important, in many cases you brain gives you wake-up call just a few minutes (or seconds) before the event.
When a weather is rainy (and thus no need to get out of cave) we sleep longer without even waking up to check it - brain knows.
When something important MAY happen and your brain has pieces of various information that indicate that it indeed may happen, it (brain) warns you (by anxiety or worriness, or other similar feeleng), and "blurrness" and strength of that feeling is directly proportional to the amount and quality of information your brain has to make that prediction.
I usually wake up sleeping students (when necessary for important explanation) not by saying something, but by sudden NOT saying anything for 5-7 seconds. Works well.
So, there is no need to attract supernatural to explain how brain subconsciousely gathers and processes information quickly and effectively.
Remember, that consciouseness is activity of only certain cells of brain (so, it is activity of only a minor fraction of brain) - thus most acquisition of information (and processing it) does not involve these cells (= takes place unconsciousely).