Influence when nobody reports to you

Most of the work that matters in an organisation crosses lines that nobody controls. A project needing three departments, a process that spans two teams, a change that requires people who have their own priorities and their own manager.

Authority would be simpler and you do not have it. What you have instead is four things, and they work better than people expect.

Credibility. Do you know what you are talking about, and do you do what you said? This is the foundation and it is built before you need it. Somebody with a reputation for being right and for following through gets agreement that a more senior person with a poor record does not.

Relationships. People help people they know. Fifteen minutes with someone before you need anything from them is the cheapest investment available in any organisation, and almost nobody makes it.

A clear case. Not what you want, but why it matters and to whom. People say yes to a reason, not to a request.

Reciprocity. Help people before you need help. Keep no ledger, and it still works.

What does not work: going over somebody's head first, which wins once and costs you that person permanently. Implying authority you do not have. Or assuming that being right is sufficient, which is the commonest mistake of competent people and the reason many of them stall.