Regardless of your positional authority, the easiest, most generous way to assume leadership is to assume responsibility for the culture.
Are you going to stir the pot, boil it over, or pour oil on troubled waters?
As soon as people learn they can rely on you not only to do the right thing yourself but, more importantly, to point them in the right direction by example, you’ll become a leader by dint of moral influence.
Many of us want to do this, but it takes a lot of practice to do it well. The best way to ensure you’ll manage the culture effectively when times are tough is to practice when things are easy. Ask yourself what you’d do in that situation, or what needs to be done that nobody’s doing. Then do it. And then, when it really counts, you’ll be ready.
The simplest definition of leadership is being on the receiving end of the question, “What do we do now?” Be ready to answer.