Let's take your idea seriously and see where it leads. You suggest that there is a being X that can understand stuff that it is inherently impossible for us to understand. So then there is some aspect of the world Y that is understood by X and can't be understood by us.
First note that proposing X's ability to understand Y solves no problems that we can understand. If we can't understand Y then we can't understand whether or not X has solved that problem. So then we can have no reason to propose such an ability.
Second the supposed existence of Y actually means that we don't understand anything. If Y exists it sometimes affects the stuff we supposedly understand and when it does so we can't understand the results. So then we don't really understand any of the stuff we understand now.
Your specific candidates also don't stand up to serious scrutiny.
The existence of God wouldn't solve any problems. Suppose that God is proposed as an explanation of Z. We have two options. (1) God made Z the case on whim in which case we might as well just say shit happens and be done with it. (2) Goid made Z the case for some reason, in which case we can just propose that reason as the explanation for Z. For example, if we say God made frogs to spread frog genes then we can just say that frogs evolved to spread frog genes.
All of your other candidates are physical systems. The laws of physics as we currently understand them seem to imply the Turing Principle: any finite physical system can be simulated by a universal computer. Our brains are universal computers and so there is no reason to think that a person can't model any physical system with arbitrary accuracy. Doing the calculation yourself might be boring and you might farm that out to a dumber computer, like the one on your desktop and then just interpret the results.
It also seems to be the case that the world can be understood piecemeal. For example, we can work out many of the circumstances under which water boils and qualitatively describe some phase transitions without understanding the physics of water molecules. We can then improve our understanding by inventing the theory that water consists of molecules in which two hydrogen atoms are linked to an oxygen atom and trying to work out the consequences of that idea. We can then understand more about different phases of water whose existence we didn't previously suspect:
You might want to read "The Beginning of Infinity" by David Deutsch, which has a lot more material relevant to your question.