First-principles thinking applies to business processes.
Starting with current state, take each step in the business process and break it down into smaller steps that are no longer divisible. For each of those steps understand what is being done and why it is being done.
Once we have the base steps we can determine the most efficient way to put the steps together to get the desired outcome.
This process is far easier to say than to do. Often, business does not realize that a step can be reduced to more basic steps. They may also have forgotten the why of the step. The majority of the thinking is in unraveling what is there.
It is typically far easier to arrange the base steps than it is to unravel them. If it is still difficult putting the base steps together it is an indication that they were not reduced enough or the why is not understood.