Not a new theory. The concept of branching time, from every individual possibility and variation, is common. But I can see that your hypothesis is not so much on the nature of time but on how humans deal with it.
How does one pick and consider subconsciously? Especially for countless little details. What is more likely is that physics and chemistry carries us through most circumstances and we only pick the things which we choose to do (and then there are those random quantum movements, but those are generally too small to be worried about). If a bullet is whizzing towards you, nothing is going to stop it from hitting you save a physical obstacle. If one of your skin cells is dying, you can't do much about it. But you can choose, say, what to eat for breakfast or what to work as.
The laws of physics would determine how most matters end up without multiple options. For example, motion, gravity, chemistry, electromagnetism. Few things are randomised. For example, quantum, radioactive decay and life. We can't control the first two, but living things tend to do what they want. This is where the Universe becomes more unpredictable, and where any noticeable branching of time would occur.
But it is worth noting that theories on time branching, as far as I'm aware, tend to suggest that time branches during the event where a choice is made, not there being a branch in the path of time beforehand.
But this is all philosophical banter. Unable to perceive time, or tinker with it, we can only contemplate.
'Cause and effect' sums up the general opinion on time. You do something, and something else will happen because of that.