If God is interpreted as "vague intelligent presence that created the universe", then I don't see any reason he/she/it couldn't exist, but I also don't see any evidence of he/she/it existing. Whereas I'm pretty sure the Judeo-Christian God doesn't exist (and I actually kind of hope He doesn't, for my sake...I have an aversion to thunderbolts), but I'm not completely sure. I'm not completely sure of the non-existence of fairies and elves, either. I'm not trying to bring that up to ridicule the belief in that particular God-I just find fairies and elves similarly difficult to either prove or disprove.
Fairies or "little people", after all, have been supposedly sighted for thousands of years in most cultures; there are a number of people in Iceland, for example, who still believe in fairies or elves, and that they still interact with humans occasionally. Maybe it's just because I come from a secular upbringing, but I don't really see the difference between elves and, say, angels. I'm not trying to belittle religious people; I legitimately don't see a difference between the two. I don't really see how believing in the literal truth of Noah's ark is any different than believing in ancient Greek mythology-perfectly sane, intelligent people used to believe those things, too. In the case of Noah, it seems plausible that there could have been a "great flood" in the ancient Middle East, but I don't believe one boat could contain two of every single species of animal in the world (including insects) any more than I believe in Zeus, or Apollo, or Thor, or any other character from mythology or folklore.
Also, I don't think any scientist believes modern 21st science can explain everything. That doesn't mean we shouldn't try, though. There are so many things about the universe that our brains may never be able to comprehend no matter how "advanced" we get technologically, but again, that doesn't mean there isn't an explanation. We just may never know the explanation. I hope that makes sense.
I do think that there is a sort of...I don't know, "spiritual malaise" or lack of purpose in, at least, mainstream American (and I'm going to assume first world in general) society. I do think people need to have something...bigger in their lives other than making money and other day to day stuff, and that's why myths and legends are still extremely valuable because of what they can teach us about ourselves. I think a person can find (or attempt to find) purpose purely through science, but I also think a more mystical approach may work better for some people. I don't know...however, I like not knowing...I think we all need to admit to ourselves that we don't know everything, and that we should keep trying to know as much as we can.