Except that it doesn't solve that problem at all. Nothing solves that problem except either an infinite deity or an infinite universe and they both amount to the same thing - infinite probability machines - one is unreal and supernatural and the other is real and natural, but both 'explanations' attempt to explain (away) the problem of an infinite regression of cause and effect (in 'this universe') by positing an eternally existing 'entity'. Neither is satisfactory IMO and the most plausible answer is just to accept that there may indeed be an infinite regression of cause-effects and that 'this universe' is probably therefore both infinite and eternal. The advantage of that is that we actually know that 'this universe' exists and we have no way of proving or disproving the existence of either an intelligent designer (unless it is a natural one like the 'Big Wow' or my own preferred metaphor for the inherent unceasing creativeness of nature - the 'eternal process pandeus') or a multiverse. All of which is to say: if there is 'design' in the process of evolution it has emerged from within rather than being imposed from without. (IMO)
I take your point, we can make a distinction between two separate paradoxes here though
what I'd call the first cause paradox- applies to either explanation, (where did THAT come from?) and so it's a wash, and a moot point, because here we are, it's obviously solvable one way or t'other
The other paradox is creation without creativity, and this is unique to a spontaneous as opposed to creative agency- whereby natural laws must be infinitely underwritten by more natural laws to support them.
Yes I'd agree we can call our creative intelligence 'supernatural' in that it can achieve what nature alone never can, and that is exactly what gives it the superior power of explanation, because otherwise
the laws of nature must ultimately be written by.... those very same laws
Creative intelligence is the only phenomena we know of, that can solve this paradox, because it can genuinely create truly novel things- unrestrained by an otherwise infinite regression of cause and effect.
And 'supernatural' as may be, it is also an entirely observable phenomena within the universe. So we have no special reason to omit it from the range of possible explanations.
Which gets to the larger point. Naturalism must banish ID from the playing field altogether, in order to be permitted to accidentally score a goal eventually.
While ID has no such need to remove natural laws to win out as the best explanation.