There just is no good inference that gets you from one to the other, and proof is never forthcoming
Now, there are a couple of facets to this argument that we should not overlook. The first is that, while the arguer might phrase it in an innocuous, non-specific fashion, the intent is rarely to defend theism as a whole, but to defend the arguer's particular brand of theism. When the atheist replies with a perfectly honest, "I don't know," the theist pounces. "Well, Allah tells us..." or "Well, the Lord Jesus Christ said..." Even if "I don't know, therefore a god" was a legitimate form of argument (it's not; more in a moment), "I don't know, therefore MY god" would take more work to prove.
Unexplained event/phenomenaIn other words, it certainly doesn't follow that allowing theism as a possible alternative leads directly to surety in one flavor of theism. That demands a much weightier burden of proof, which is never met. The intent, of course, is that you should consider the two alternatives ("I don't know" and "well, maybe a god did it") as equally meritorious, thereby admitting "maybe a god did it" as a viable solution; and somewhere along the way, with absolutely no justification, jump from "a god" to "my god". This is ludicrous, as allowing for the viability of the god concept does not in any way prove the existence of specific god(s). But "I don't know" and "a god did it" are not equally meritorious answers.
| (anything unexplained must be the result of a god)
My god did it
In the past, religious institutions have relied very heavily on "god did it". In times of more primitive technologies and science, this was an eminently successful strategy. Consider the vast range of items the Church (and most other religious bodies) attributed to their god(s). Everything from the common cold to weather patterns, plagues and pestilences to wealth and good fortune, spoiled ale to a healthy newborn, came down to god (or demons, that could only be defeated with more god). The less we knew about biology, the more we attributed to gods -- the more churches attributed to gods. The less we knew about our planet and other planets, the more we attributed to gods. The less we knew about any given branch of science, the more "prayer", "repentance", "God's favor" and "God's anger" mattered. Nowadays, we don't much worry that a loud thunderstorm means that we've pissed off some extraordinarily temperamental divine; but at points in history, people cowered in terror over just such a meteorological event, the words of a pious priest or wise shaman echoing in their ears. Even in this day and age, when science explains so much of our weather related phenomena and natural disasters, we still have the odd preacher, rabbi, or imam who tries to sell them as part of the divine anger and godly retribution package. (If you're curious, according to religions' snake oil salesmen, temperature shifts, tectonic plate shifts, etc., are more or less irrelevant...hurricanes happen because dudes hold hands, and earthquakes are the result of tank tops. See, who needs science?!).
In general, though, it's ignorance that provides the most fertile environment for this reaction to develop: while some people will cynically view a natural disaster or tragedy as their merciful god's message delivery system of choice, most of us cede to the science of the event. Because now we know the how's and why's. We can understand the progression of illness, and we don't need to fallback on "God's wrath" or "demonic possession". Where religion once had a monopoly on the plentiful swath of human concerns, science has, a piece at a time, wrested that control from it; prayer and tithing might have been the best answer to most questions during the dark ages, but now science provides practical resolutions and sensible answers to those same concerns. Indeed, when we look back at the long history of man's superstitions, we see that "god", "demons", and "more abject fealty" were never really the answers after all.
That is why it is so surprising when people fall back on the same ineffective line to explain matters that science hasn't been able to adequately address -- yet. It calls to mind Albert Einstein's definition of insanity: doing the same thing over and over and expecting different results. In this case, it's resorting to the same non-answer and expecting a different result -- its accuracy. "God", while invoked for just about every question man has encountered since the beginning of time, has never been the answer. We've never had an instance where we've encountered an unknown and discovered that, at the end, "god" really was the answer; no matter how impossible a solution seemed at the time, eventually our species discovered it. What recommends "God", then, as a best solution? Absolutely nothing beyond wishful thinking. No evidence, no compelling philosophical reasons; it's just a fallback, a baseless substitute for "I don't know", borne of wishful thinking, masquerading as something more, and conferring a false sense of surety as it goes.
"I don't know, but we're working on it," is the most accurate and honest answer for the question of "how did our universe come into being." And, incidentally, it's the only answer to these sort of questions that has ever borne fruit. "God" is the answer that nets no further examination; "I don't know, yet" is the answer that demands further investigation. Frankly, if mankind had been content to accept the former, we'd still be in the dark ages; just about every branch of science, all of our life saving medicine, etc., would have been lost to the "God" vacuum. Indeed, "god" has been the answer that historically has slowed humanity's progress; it's the answer that got scientists burnt at the stake.
So seeing people throw out "god" as a response to the questions of the universe's origins is not reassuring, and answers exactly nothing; it's simply shades of past follies: exploiting a knowledge vacuum to substitute the desired answer. And, sadly, it is an act that confers an entirely undeserved confidence on itself. It's the true deus ex machina, something humanity has been doing since time immemorial: instead of solving the problem, invoke a god, thereby producing an answer that is at once unproven and unprovable. We live in a world that should, by rights, render such an argument (at least, arrived at in such a fashion) laughable -- because our success and progress is directly attributable to people moving beyond "because god" to understand why, really. And yet it's still trotted out with all the false surety of the most superstitious snake oil salesman of yesteryear -- and with not a lick more proof...