I'm not going to respond to "science doesn't know everything" and "you can't prove there is no God" portions because they are too philosophically elementary, and have been responded to a million times over.
I will point out the contradiction in your thinking though. You make two conflicting points. First, science does not rule out a creator because our understanding has limits. This is a materialist stance. You are saying that given a sufficient level of understanding, a hypothesis about the nature of God can be advanced. God is thus an ontologically natural phenomenon that can be understood. Later, you make the claim that God's existence does not fall into the bounds of scientific inquiry and must be left to religious belief. That's an immaterialist argument for God.
These are mutually exclusive arguments. I can easily respond to either point, but not both at the same time. Make up your mind.
And I will point our the unrealistic simplicity of your dichotomy.
In asserting that there is stuff we cannot access with our senses or scientific tools, I don't necessarily assert that it is immaterial, just inaccessible. Read up on Quantum Physics. We are still trying to design and build better tools for detecting material particles which our mathematics demands must exist.
Mormons have long harbored notions of "spirit" being a kind of matter that we cannot see or detect with our common tools of discovery, and in times long past have theorized that all living things have unique spirit forms, and that even inanimate stuff has a spirit form as well. However, the specific "God" Mormons believe in is distinctly and unequivocally material. The only thing we lack is a science with a power of subpoena which could command God to appear and submit to examination.