Cobweb,
To understand the Jewish take on God you have to abandon two concepts you kept repeating: belief and the idea that the God of Abraham is a deity.
Christianity is a religion of belief, whereas Judaism is a religion of practice. While Jews do indeed have convictions, they act on them instead of put faith in them. A practicing Jew can be agnostic or even atheist yet at the same time pray and accept the reality of God. How?
That has to do with the second point: YHVH is not a deity. There are no such things. Those are inventions of humans. The universe is a product or effect of a Cause. That Cause is the God of Abraham.
Just as we adopted the names of gods that our concept "conquered," the word "God" is no different. The Cause is so great that it is ineffable, unknowable, inconceivable. And yet this Cause appears to interact with us. We are aware that the world has not always been here. It had a Beginning, and the universe is governed by laws.
This is what Abraham came to realize and passed down to his progeny. Pagans worshipped gods, but the Hebrews felt nothing but this Cause deserved the credit that the pagans gave to deities. At the same time they wrestled with the idea of worship and blind obedience. This became seen as enlightenment. The Hebrews were not to be blind worshipers of the Cause but work in cooperation with the Cause in a partnership.
The partnership is the covenant. The scientific laws that govern the universe is Torah. Torah has a human facet to it. Humanity suffers and causes suffering when we ignore it, just as much as when we ignore the physical laws. The Torah written in Scripture is an early attempt to understand these laws, but they are just very early and fuzzy glimpses of it. So Jews don't follow Torah as written in Scripture. They use it to see Torah clearer in each successive generation.
Because the physical universe is real, the Cause is real. Because we can learn the scientific laws and can tap into laws that seem to benefit humanity (such as being just, honest, respecting the rights of others, etc.), Jews understand this as tapping into the "Divine," so to speak.
Lastly, Judaism is not based on the Scriptures as an authoritative text. Scripture is a product of Judaism. The practice of Judaism is the authority.
The above is very simplified. It can cause headaches for some. This is also very generalized as Jews don't have a central creed since we don't believe in giving mental assent to concepts (such as having "faith" in a doctrine like Christians). Some of this spells out exactly how I practice Judaism but some of it reflects that of others and not my own.
Basically speaking, since this world, the effect, is real, thus so is the Cause. Therefore God is real. Just as I don't believe in the world as it is here and doesn't require my belief to be real (it just is real), the same can be said for my position on God.