I had a discussion like this with a seasoned professor. I think the best and also simplest thing to do when tackling a new problem is to first figure out multiple ways you think you could solve it WITHOUT doing a literature review. That shouldn't take too long, and doesn't involve actually doing any research, just some thinking and maybe some basic reading (but not a literature review). Then, review the literature, at which point you'll see if your ideas have been tried before and \ or have merit, based on your improved understanding.
What happens a lot in science is that people acquire a lot of knowledge in a field, and then often creativity is stifled, as every solution to a problem is seen in the light of the existing knowledge. It's hard to think originally about a problem when you've seen lots of other attempts to solve it. I call this the 'burden of knowledge'. So I would encourage contemplating a problem yourself before seeing what other people have done. This may lead to an original line of inquiry. But preferably before you spend a lot of time doing real research, do a thorough literature review. You'll also find that contemplating how to solve the problem yourself will help you understand the efforts of others better.
One more thing. In the field of mathematics at least, it has been commonly noted in history that some of the greatest mathematicians solved some big problems in their youth, before realizing that others had already solved that problem. I specifically recall reading this about Alan Turing, but he wasn't alone in this. Sometimes this may lead to alternate proofs that are more elegant or reveal other mathematics. For instance, Andrew Wiles solved Fermat's last theorem using tools that didn't exist in Fermat's day. So assuming Fermat did in fact solve his famous last theorem, then there is likely a much simpler solution which may reveal new mathematics. So sometimes solving an existing problem in a new way can be very valuable in its own light. That may be true even if your solution is not more elegant or more effective, if it's shows new lines of inquiry.