Complementary, and considering the answer of António José Rodrigues Rebelo
I think you could organize your ideas in an Ishikawa diagram to have a clearer picture of the problem and concretize to a specific factor in the mentioned problem has proved to be too complex.
Regarding your question, it is difficult to consider solving a problem if the problem has not been identified as such. Unless we consider that sometimes when changes occur we realize that the new configuration is better, and therefore that we had a problem that we were not aware of before.
On the other hand, it is common to resolve problems without even determining the root cause. This occurs in situations where the causes are hidden, where information is insufficient or where complexity is high. This exists in many areas. For example, in medicine we can solve a problem with lichen on the skin without knowing the root cause of its appearance. Between "identifying the problem" and "determining the root cause of the problem" as the first step in problem solving, I would say that in the absence of a definitive answer, "identifying problem" seems to be more frequently applicable than "determining the root cause".
However, it is important to note that the boundary that determines the first step in problem solving can vary considerably from one domain to another. Overall, problem solving can be distinct from problem analysis (diagnosis, problem caracterization...). The boundaries between these phases can sometimes be blurred, and there may be many iterations between problem solving and problem analysis for various reasons. Despite this, it is possible to consider that "problem identification" and "root cause investigation" are not strictly steps in problem resolution, but rather steps contributing to this resolution.
In fact, when these steps are integrated into a problem solving process, it is often with the aim of improving the quality of the resolution, as they can contribute to a better understanding of the problem. For example, while we might solve a problem using reflexes, heuristics or intuitions, adding the "root cause identification" step aims to move beyond these reflexes, heuristics or intuitions and hope that the Identifying root causes helps improve the quality of resolution.
This is my thinking, although it is not academic and has its limits. It is possible that researchers in applied epistemology could provide a more structured reflection than my intuitions.