In every group project, someone opens the blank doc and types the headings. That person is already in charge.
LEADERSHIP
LEADERSHIP
Authority in a loose group goes to whoever reduces the uncertainty first. Typing the headings is not an impressive act, and it converts a vague pile of worry into a shape other people can work inside, which is most of what leading consists of. Whoever does it rarely intended to take charge and simply could not stand the blankness.
Be the one who makes the first structure this week, even a rough and obviously wrong one. Invite people to change it, and they will. Being easy to correct is what keeps this from turning into a takeover.
In your last group project, who opened the blank document?
Free, with nothing to buy inside it.