Ask who is responsible for a process and you will get a list of steps with a name against each one. Intake is Maria. Review is the committee. Approval is the director. Filing is whoever is covering the office.
Now ask who is responsible for the space between review and approval. That is usually where the week went.
Everyone did their job
This is what makes it hard to see. There is no one to correct. Maria completed intake. The committee reviewed it. The director approved it the day it reached her. Every person can account for their own part, and the thing still took eleven days that nobody can explain.
The time is in the gaps, and the gaps have no owner. A step has a name, a definition and someone who will be asked about it. A handoff has none of those, so it belongs to whoever notices.
Two questions that find it
Take something that moves too slowly and ask, for each transition: who is accountable for this item between the moment it leaves one person and the moment the next person starts on it, and how does the next person know it is their turn.
If the answer to the second question is that they check periodically, or that someone tells them, the handoff is running on attentiveness. That works until somebody is on leave.
Decide what finished means
The fix is usually not a new system. It is deciding what finished means for each step, in terms the next person can verify, and naming who is accountable for the item until they pick it up.
That single change removes most of the waiting, because waiting is rarely somebody being slow. It is an item sitting in a place where nobody has agreed it is theirs.