(Personally, I don't mind a "God of the gaps" model, because the more we try to fill in the gaps, the more we should realize how vast they truly are; the more Christlike we become and the more work we try to do for our own salvation, however successful we may be, the more we realize how inadequate we are for the task without Help.)
It's the same argument the scientists are making against proponents of intelligent design. The proponents play with scientific tools, trump up some evidence that suggests we must have had a creator, and then insist we teach this version of "science" that explains the First Thing fairly well (or barely well at all, which I'll get to in a minute), at the expense of being able to explain anything else coherently.
Good science is not entirely dissimilar to Catholic theology: it's a seamless garment. You can't add or subtract anything, or change the rules-horses midstream, without endangering the whole item to unravelment. Is unravelment a word? It should be.
First, there is such a thing as the Anthropic Principle. Things are configured in a way that permits us to observe them; if they were not, we would not be here to be making the observation. Someone else might, though. The universe might have been anything, but it had to be something.
Being a man of faith, I am in a sense a believer in intelligent design, but I will not sign on with the likes of the Discovery Institute. I am unable to reconcile an assertion that, while it should be impossible for me to see a piece of bread and a cup of wine turn into the Body and Blood of my Lord because He wants me to have faith in the matter, it's perfectly legitimate to assume I can find empirical evidence that God made things if only I had clever enough technology.
There is also a question of who the Designer is. Some ID proponents say "Aw no, we don't mean 'God' like you used to hear from those Young Earthers! I'm just talking about...aliens! Yeah, panspermia! Exogenesis!" It's a fascinating concept, but I'll stick with the Young Earthers (which is not to say I'm a Young Earther myself, in light of the current body of evidence), because I know they, at least, are being honest with themselves. If life was too complex to have developed here, such that it had to have come from somewhere else, how could it have been simpler somewhere else in the first place? Were the aliens who seeded Earth seeded by aliens before them? Are we going to have to assert it's turtles all the way down, or come clean and admit that God tipped the first domino somewhere along the line?
Either way, it's good to recognize that science and faith have different bailiwicks, but if we're going to impose on one with the other, we should recognize we're not doing anyone any favors. Touting science's inability to gauge God as proof that there is no God to gauge might be an amusing philosophical parlor trick but it's not science, nor is it faith (I might even argue it's not even honest atheism, but I don't want to open that can tonight). Dressing up some preconceptions with statistics and claiming veracity on the grounds that their interpretation can be theistically ambiguous is not science, or faith, either.
Why isn't the Eucharistic miracle good enough? If you're not even willing to admit to the sacraments, shouldn't your faith already be too strong to need such crutches, or too weak to accept the problem in the first place?