Find the work between the steps.
A process chart is only useful if it reflects how work actually moves. Follow one request from start to finish and note handovers, queues, rework and unclear responsibilities.
Improve a bounded process
Choose a manageable problem, describe the current state and agree how improvement will be observed. Small experiments can reveal constraints that a large redesign would otherwise overlook.
A useful starting point
Write a short note describing your situation, the question you are trying to answer and the evidence you have. Keep it specific enough that someone else can understand the decision without guessing.