I'm in agreement with you that the Genesis account is not symbolic, but not because I think it's historical - because I think it is a wrong guess like all creation stories (apart from the scientific account).
A wrong answer is not a symbol. Nor is it an allegory or metaphor. All of those imply substitution of a symbol for something literal. The five Olympic rings are symbols representing continents. An apple is a symbol for something appealing and desired in, "She was the apple of his eye." Gulliver's Travels is an allegory in which fantastical fictional characters substitute for prominent figures in British politics of Swift's era.
But these creation stories don't stand for anything but wrong answers, like misadding a sum of numbers, and then later, when somebody comes along and adds them properly, we are told that the old sum was a symbol, that is instead a timeless truth and life lesson not to be taken literally, and that scripture is not meant to be understood a math book (or science, or history).
I think mistake is a better description, unless one wants to believe that scripture doesn't contain errors, in which case he must find other words like symbol.
Maybe your question should be how one knows the Genesis account is incorrect. That's a longer answer, but in a nutshell, science has shown us that the story is incorrect. If you want those answers - what scientists have determined to be the case and the evidence supporting those tentative conclusions, you'll need two things: skill in critical thinking and a basic understanding of science, meaning you'll need to develop those things to have access to those answers.
But the good news is that millions before you have done so. One has to value such knowledge to make the effort to obtain it. My experience with creationism apologists is that they aren't interested in the science even when they ask about it. They don't do even a cursory survey of the Internet for information, and if one provides them with links, there's no evidence that they've even opened them much less made the effort to try to understand them.
That's how I know that the Genesis account is incorrect: I've learned the science.
That is incorrect. If you don't have the data base and the critical thinking skills to recognize and accept sound conclusions, everything looks like unsupported belief (faith) to you.
There are other ways of thinking, other methods for deciding what is true than the simple willingness to believe, methods involving belief by reason applied to evidence. If you're unsure whether these are both faith, note that there are over 40,000 denominations of Christianity alone, a faith-based activity, and just one periodic table of the elements, derived from the proper application of reason to physical evidence.
Of course, recognizing evidence is also a problem for the faith-based believer, as when we are told things like what you just wrote, that belief in evolution is faith-based, or that trust in science is not different than trust in God. The difference is the evidence for the scientific method - it stunning successes. To claim that it's all just faith that got man to the moon and back is to ignore the evidence that the success of the missions provides in support of the assumptions underlying the design of the mission.
So, no not the same, even if there are some who are unaware that it is possible to think without faith. One can train oneself never to swallow an idea unexamined as surely as one can train himself not to swallow unexamined food. One can learn to apply the smell test to ideas as well and recognize and reject unproven ideas for their failure to meet the criteria for justified belief.