It's not a gap because it's not a scientific question.
It's not a question at all.
There is no realistic chance science will ever be able to adequately explain what came before the big bang,
Science has no theory about any past unobserved event. The Theory of the Big Bang is not a theory of science.
The Theory of the Big Bang states that the Universe began as an intense point of energy and matter, exploding into what we see today.
The cause of this event is not descrbed. Any cause outside the Universe is itself a paradox.
nor to explain why the rational mathematical laws of physics exist or where they came from.
Buzzword fallacies (rational). Redefinition fallacy (theory<->law).
Redundancy (math->math).
Mathematics was created by Man.
Every theory of science was created by Man.
Every law of physics is a transcription of a theory into a mathematical form. That equation is called a 'law.'
No theory can ever be proven True.
A theory of science CAN be proven False.
A circular argument cannot be proven True or False.
It's a philosophical question that is posed by the existence of known physical properties of the universe.
You deny philosophy here. Circular argument fallacy (fundamentalism). The Universe is unorganized.
The scientific laws and theories we already know about practically beg the question.
Fallacy fallacy. No theory of science is based on any fallacy. Science does not govern anything. Science is not the Universe. The Universe is unorganized.
We can use logic and reason to rule certain things out.
You deny logic. You apparently never learned it.
At the level of nature, you have never seen something come from nothing (at least where it violates laws of conservation), you've never seen the rational come from the irrational,
Random words. No apparent coherency. Go learn English.
you've never seen lawful organization come from randomness and chaos.
Organization is not 'lawful' or 'unlawful'. It is simply organization.
Yes, it is quite possible for organization to come from chaos. Every time someone builds a car, a computer, a watch, a phone. That is organization coming out of chaos.
Organization is not matter.
Organization is not energy.
The Universe is unorganized. The Universe is not a car, a computer, or a watch.
From there, it's not a huge leap of logic to infer some kind of immaterial rational agency underlies the organization we see in physics and cosmology.
Non-sequitur fallacy. Buzzword fallacies. You are denying logic again.