But with the question as asked
"The Universe began 13.8bn years ago, with a big bang"...
...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.
How does it imply that? It just says "The Universe began... with a big bang," without saying anything about the mechanism of its creation one way or the other. I can talk about
Star Trek without mentioning Gene Roddenberry. I can talk about making a phone call without stopping to remind people of Alexander Graham Bell. But that doesn't mean I'm claiming they didn't create those things. I'm just not bringing it up.
And it would be inappropriate for a statement about science to mention God in any case, because science is only about testable hypotheses, and the involvement of a deity in the creation of the universe is a matter of conjecture or belief. Leaving it out of a discussion of science is not a rejection of the possibility, merely an acknowledgment that it's a matter which science does not address one way or the other.
Second, as a scientist, I don't "believe" anything of a scientific nature.
It doesn't appear to me that the survey uses the word "believe." It's phrased in terms of the respondents' confidence in the statements given.
Of course, it's a badly worded statement, saying the universe began "with a big bang" without defining what that means. Of course, it did not begin with a literal big bang, but with a burst of inflation; "Big Bang" is just a facetious nickname. So that phrasing itself may have confused people and increased the percentage of "not confident" results.
Evolution isn't a theory.
Evolution IS a theory. It's the mechanism for the origin of species.
Evolution is an observed phenomenon. Evolutionary theory is the body of laws explaining how and why it works. In the same way that the theory of gravitation is a body of laws and equations explaining the observed phenomenon of gravitation, music theory is a set of principles explaining how the observed phenomenon of music works, etc. The problem with saying "Evolution is a theory" is that it confuses the thing itself for the model that explains it. Evolution is a documented reality, and it is codified and explained by evolutionary theory.
The lay belief is that theory is something less than fact. But it's the other way around in scientific terms. A fact is merely an observation, a data point. A theory is something that encompasses a body of facts and explains the reasons behind them and how they fit together.