The are several grand buried assumptions in that question. The first is, what is meant by “all this intelligence in nature”? We observe that life replicates and mutates, and that is the driver of natural evolution. So we may observe that the naturally occurring Alu retrotransposons (parasitical genetic elements that carry a “copy me” signal in their coding) have proliferated in our primate lineage, so that in our case about 10 percent of us is a pile-up of Alu copies (around a million and a half and growing). Was any of that intentional? If all of it were intentional, that is awkward, since when occasionally Alus mutate and add a “read me” signal that causes their activation, the effects are usually bad (screwing up protein folding, for example).
Though once in awhile, luck of the draw, some effects turned out to be beneficial, and chunks of our brain systems now draw on elements contributed by those pesky Alus. But there’s no need to attribute any of the Alus (good or bad) to purpose, they just are, doing their thing in the busy surging dynamic exchanges that is our biology. Those who seek to see “intelligence in nature” may not have looked as close at the nature as they should have.
Which brings us to the second buried assumption in the question. Which “God” did they have in mind? Remember, whichever deity they embrace, most of the people on Earth don’t currently share it, and never have. Every version is a temporary minority belief (even if in, say, the case of Christianity, you get a sizable 2.6 billion minority if you lump all Christians together as a bloc, even if they aren’t always willing to do so themselves).
So how do you distinguish the handiwork of a purported deity in the past or currently? There are no designer labels in the biology to help, and there’s another snag: no religion had ever laid out an explanatory narrative of the past that even remotely matches up with what we’ve determined by science. Religions easily had the earth as flat (took a while for the Greeks to popularize a spherical one, and got folded into Christian lore), occasionally some had durations in the billions of years (like the Hindus, who invented zero in math and got carried away with it), but just as hyperbole, not historical reality.
No religion described a cosmos starting out only as stars lacking solar systems, going through multiple supernova cycles to spread the raw materials for our generation of stars with planetary systems, or that when life appeared here, it was exclusively bacterial, taking billions of years before colonizing the land, and along the way manifesting no bee-line rush to get to humans who could build cathedrals to specific gods.
That mismatch between the religious baggage and the observable science is a major problem for those wishing to shoehorn in their parochial “God” of choice, to the exclusion of all others, as if the sacred texts had clearly and uniquely explained things in a way showing the author had access to the full factual skivvy.
And of course the “natural theology” approach to verifying particular gods, not be defending their overall content, but by trying to end-run with allusions to the wonders of nature (without necessarily studying it closely) doesn’t make the moral theodicy problems go away. Religions have a questionable track record on human rights issues, from the treatment of women to their willingness to go along with slavery. None of that historical reality goes away, however much “intelligence” one tries to tease out (selectively) from the nature kit.
While there is no official doctrine on reading books from other faith traditions, members of The Church of Jesus Christ of Latter-day Saints have long been encouraged to seek out learning as a lifetime effort, this often includes reading things beyond our own canonized scriptures or the modern words of our Prophet, Apostles and other Church Leaders.