For many scientifically literate Christians the way the question was asked takes God out of the equation and IMO they lose confidence.
Had the question been asked separately as well, " ~ 13 billion year ago, God started the big bang and the universe unfolded and man came about through natural selection...," the number of respondents who agreeed would have been higher.
The Catholic church for example embraces a 13 billion year old universe, the big bang and natural selection. They just also believe that God lighted the match that started the whole process with the intent for man to be eventually created.
But with the question as asked
"The Universe began 13.8bn years ago, with a big bang"
Does it matter if a person thinks God started the universe 13.8bn years. If they think 13.8bn years ago God started the universe with a Big Bang they could still answer in the affirmative. Isn't a negative answer basically saying I don't believe a big bang occured (no matter how it started)?
Yes, actually it does matter. Take me, for example. I'm a scientist who spent many years in graduate school earning a Ph.D. in Biochemistry and Molecular Biology. I also have more than a passing interest in physics and other sciences relevant to the survey. Yet I am also quite religious and firmly believe that the universe was created by God. I am most decidedly not a young-earth creationist. When I read that question I was brought up short and I don't think I would have answered that question as "Extremely/very confident", and possibly not even "Somewhat confident". That is not because of some belief in a literal interpretation of the Biblical account of the creation (I don't), but for a couple of other reasons.
First, the way it is worded strongly implies a God-less creation, at least to someone who does believe that God had a hand in it. I would have difficulty answering the question at all because it seems to setup a false dichotomy of either a God-less creation or a young-Earth creation.
Second, as a scientist, I don't "believe" anything of a scientific nature. I accept or reject hypotheses based on data available. Regarding the Big Bang, I don't "believe" it, but I do accept it as the best available hypothesis with the data currently available. Saying that, though, there's still a bit of faith there because I'm not a physicist; I'm only basing that acceptance on the word of those who have the data and the expertise to analyze it. That wouldn't be true of topics in my own field because I am capable of looking at the data and interpreting it for myself and deciding whether or not I accept the conclusions offered, but on the topic of the Big Bang, I only have their word to go on. I can't say I believe it, or even have high confidence in it; I can only say that it sounds good to me because those who do have the expertise say it's the best explanation and I have to take their word for it. Since I don't have any better ideas or data to contradict theirs, I go with theirs. That's really all anyone (other than those who do have the expertise, anyway) can say, so anyone who does say they are "Extremely/very confident" doesn't understand science and is putting more faith in scientists than they should.