You're absolutely right to feel that your time in the early stages is best spent understanding the problem.
Mapping the use cases and data/control flow of the requirement is one good way of building up that understanding, and in doing so, you are also testing those requirements as you will discover questions that you want to ask, gaps and ambiguities that need to be clarified.
I would suggest that you also step back from the requirements doc and spend time understanding what value the system under test is meant to provide. This can be surprisingly hard to uncover by simply looking at lists of requirements - you may need to follow up with business analysts, or other representatives of the business to understand the motivation behind the requirements. (You might find that the business isn't actually all that clear about what value they want, or that different stakeholders have wildly differing and contradictory views on that. Be diplomatic here, and bear in mind your company culture. In some companies you'll be thanked for uncovering this kind of problem, in others, not.)
Without understanding what value the system is meant to provide, however, you don't have any way of designing your tests so that they are most likely to reveal risks to that value. And that is what your testing is for, isn't it? Not just to unquestioningly confirm each requirement and go no further?
Something else that I seek to do in early stages is to gain an understanding of the technology, especially if it's new to me. The depth I go to depends on the project - some require that I build up a reasonably good technical understanding in order to identify risks, others don't. I'm not just looking for risk though when I'm doing this - I'm often trying to understand what tools might be useful to me for exploring the system. Sometimes I write some of these tools ahead of time. I also think about what test data might be useful, what test environments I might require, and so on.
All of these things are more valuable than spending time on documenting something that you don't yet understand well enough.