I'm in the process of making new print books for both the WAR and the SSU series.
Here's a video describing the process:
Once I approve the proof copy, it goes live, which can a few days up to a few weeks, depending on the retailer.
My books are print-on-demand, so they're only sent to the printer when someone orders a copy. My book is then added to a batch of other books to be sent through the printing machine.
The below video shows Amazon's printer preparing a batch of books.