In the near future, how often do flights depart to Luna?
Right now we don't have an active Luna program. Back when there was one, the answer was "about once per year." I think it is a safe assumption that the parcel will travel on a regular scheduled flight.
If those depart once per week, there is a delay of 0-6 days from scheduling.
How long to package the cargo?
Right now things which go to space are checked in different ways for safety, designed for low weight, carefully stowed, etc. That takes weeks or months.
By the time we're talking about an Amazon delivery, obviously shipping stuff to space has become more routine. How much more routine? Can I order a can of beer? A lawnmover? Let's say packing the crate takes a day.
Transfer in orbit?
The Apollo missions launched the complete package from the Earth surface and discharged expensive vehicles at each step. A "mature" system would use a reusable shuttle to a transfer station in Earth orbit, a reusable vehicle from there to another transfer station in Luna orbit, and finally a reusable lander to the surface.
If the same flights carry cargo and passengers, the delays won't be too long. If only cargo is carried, it might sit in the transfer stations for a couple of days each.
The pure flight time is the smallest problem.