but why does god offer a plausible explanation at all?
Because it is very similar to something we know already, with a similar end product: a human designer. That is why it sounds plausible.
With regards to the snowflake, and many other beings, death material or alive, that come to exist without any external influence, it does not answer the questions about how the complicated circles of life in nature came to exist, with other words, who or what designed the conditions that make snow flakes build themselves? To name just one, strictly related to the snowflake, why is the specific gravity of ice lower than the SG of water, making ice cover the water and not sink in it? Most other "solid" materials are multiple times heavier than their "fluid" form. Why not so with water? Is that one of many "very lucky" but hard to explain coincidences? Can it have developed over millions of years? I think the answer is no.
In the ultimate machine design, the end product is produced continuously without any external adjusting influence, as long as the raw materials and the power supply are continuously provided. Systems in nature are very similar to that.
Yes, I absolutely agree that nobody has built the snowflake in the picture, but that proves or disproves nothing at all.