I'm a first year PhD student in theoretical physics. My problem isn't strictly due to imposter syndrome, but rather not knowing how I should be spending my time. My supervisor has only given me some vague guidance on what my project should be about, while I hoped to be given some reasonably well-defined first problem to work on. His most concrete suggestion was along the lines of "go study some lattice model on this particular class of lattice geometries and see if you find something interesting".
For the past two months, while trying to follow his suggestion, I have been attempting to learn various methods that might be useful to my project, allowing me to study said models in said geometries, or to at least gain a better understanding of the available literature, but that's not a way to continue; there is not enough time to learn even a handful of methods that would be relevant to the problem at hand in sufficient depth. I've only had a couple of ideas of how I might be able to study the problem emerge during this process, but even then I don't know if those ideas are feasible, let alone sound (and the more I think about them, the less sound they appear).
My supervisor isn't actively doing research himself, and only engages with the research being done by the people in the group through meetings, which is unlike some other group leaders I have done projects with. I appreciate that my supervisor gives me full independence in choosing what I want to work on, but identifying a suitable problem to begin with and means of solving it is what I struggle the most with. Other PhD students in my group are lucky to have co-supervisors who seem more engaged with their projects, or had been supervised by a postdoc during their Master's project and now have some clear follow-up problems to work on with their postdoc partner.
Is this how PhD research is expected to look like at the beginning, or are those signs that my supervisor is not particularly good at supervising? I'm in the UK, so changing my supervisor is not an option.