Proof of G-d
Could you please present a brief and convincing proof for the existence of G-d?
In a nutshell, you’re asking for a lot.
But even if I weren’t constrained by your request for brevity, I couldn’t give you a conclusive proof for the existence of G-d. That would fundamentally negate free-will.
However, I will try to present one of several arguments for a rational belief in G-d.
Existence is not an illusion. It really exists. Existence doesn’t spontaneously come into being from non-existence. It might be coagulated and formulated from a composite of pre-existing parts, no matter how small. But this sub-matter, or even energy, is subject to the same dictum: it cannot spontaneously bring itself into being from nothing. This dictates that something brought Existence into being, ex-nihilo.
This Source or Cause of all existence is referred to in Judaism as G-d, the Creator.
Since G-d created space, the place of Creation, including time, which is merely a function of space, it necessarily follows that G-d precedes, is independent of, and outside space and time. In this way, G-d is non-finite — Infinite. The Creator is therefore unlimited by space and time, and exists everywhere at all times, with no beginning or end.
By the way, this does not contradict what I posited earlier, that existence must have a beginning, because that applies to physical matter and energy, but such limitations cannot be applied by the limited to the Unlimited.
Further, it follows that there can be only One such Infinite Creator. And even though we can conceive of multiple parallel infinities, conceptually represented by, for example, parallel lines, of which there may be many, or even an infinite number of simultaneously existing infinities, since this is limited to only one plane, it at most describes only “relative” infinity.
However, the “infinity” of the Creator is absolutely infinite, better represented by the unquantifiable totality of such infinite parallel lines, not on one plane, but on an infinite number of intersecting planes. This mathematical representation of the concept of absolute, all-inclusive “infinity”, which not only contains everything, but actually is everything, is what we’re referring to when we refer to G-d.
Jewish mysticism explores and explains how both the realm of “relative infinity” (corresponding to the spiritual, non-physical realm) and the realm of the physical and finite are actually even able to exist within the absolute “infinity” of G-d rather than dissolving, imploding or reverting back into It.
But since you asked for brevity, I’ll leave this dimension of the discussion for another time…