This might bespecific to your discipline, but I think you do have a misconception about what your aim as a PhD student should be. The aim is to do research and provide new insights into your field based on scientific methods.
To me, the fact that you have started a PhD position without a topic is a bad sign. Your supervisor should either have given you some ideas or asked you what you want to do research on when you applied. Imo if neither of those has happened you should seriously reconsider whether he is suitable supervisor to your (or anyone else).
Now given that you are in this position anyway and you might not agree with my opinion here, I would give you the following advice.
If you are searching through literature for problems to solve, try finding out if review papers are common in your discipline. Those usually are very long papers which give a great overview over a field once there has been substantial progress and if there are known experts around. These are to my experience more likely to make you aware of open questions and unsolved problems than other types of papers.
If you are working in social sciences it might also be helpful to search your own head. What I mean is: Why are you interested in this field? Which open questions do you have? What did people fail to explain or prove to you during your studies?
Again for literature review I would focus on more recent problems and publications. Often you will find that you can use methods old methods and apply them to a new field which they have not been explored in. This gives you a quick start into a topic and once you start doing research on your own more interesting questions might pop up.
If you have done all this and figured out a general area of interest, go talk to your supervisor. You should do this either way. Again he does not necessarily have to come up with a very explicit suggestion, but anything that gets you to start working on a topic where he - or some of his close colleagues - have a good level of expertise might open exciting questions for you to work on along the way.
The same could also happen if you start collaborating on something with another PhD student or postdoc. I really advise against pure literature review for the search. Personally I couldnt keep that up for more than 2 weeks straight.