The short answer
God certainly is not needed for unanswered scientific questions right now. Perhaps this eventually will change, although it is not clear how introducing a god into the picture would help with any questions unless one lowered the bar for explanation all the way to the bottom.
The longer answer
I. Naturalism’s track record
Science has an outstanding track record of solving unanswered questions without invoking the supernatural, though the solutions often take time. Had scientists immediately thrown their hands into the air and bowed to supernaturalism every time they came across a tough problem, we would still be blaming mental illness on demons and low crop yields on witchcraft. Considering naturalism’s outstanding track record, it seems only prudent to let scientists continue to seek naturalistic solutions to the current unanswered questions. Should any of those questions ultimately require the introduction of a god, one may rest assured that mainstream scientists will abandon naturalism on their own, just as the spectacular failures of supernaturalism over the last 500 years have led scientists to gradually abandon it for the far more productive working hypothesis of naturalism.
II. What would the introduction of a god accomplish?
Putting aside naturalism’s accomplishments, one of the challenges that faces those who would try to invoke a god to answer current scientific questions is that it rarely, if ever, is clear how introducing a god would help. Too often, the creationist approach is to try to find something that science has trouble explaining right now, and to say that this shows that creationism is true. But when asked how creationism explains the difficult phenomenon, the answer amounts to little more than “God did it somehow.” But if the bar is set so low that “God did it somehow” counts as an explanation, then it is difficult to see why “It happened naturally somehow” would not be just as good an explanation. This is why scientists complain about the fact that creationists seem not to be interested in developing theories to contend with the current mainstream ones: if all creationists do is point out gaps (whether real or imagined) in current scientific knowledge, creationism never will be taken seriously, because it does not have anything better to offer.
I would not go so far as some of my colleagues, who claim that invoking the supernatural never can be explanatory, or that they cannot even in principle be a part of science, but it is clear that supernaturalistic explanations need a lot of work if they ever hope to compete again with naturalistic ones.