What equipment and tools can be used to fabricate an 8 layer PCB for a prototype that has a 584-BGA microcontroller
Advanced PC boards can only be made by little elves in a hollow tree.  It is possible for ordinary mortals to make good enough 2 layer board for hobby or prototype purposes, but even that doesn't make sense unless they value their time very little and not look too hard at the cost of screwups due to not having a solder mask, silkscreen, and the hassle of not having plated thru holes.

Anything beyond basic two layer boards requires elven magic.  The elves have spent millions on special trees and are constantly watching the process.  Due to the combination of up front cost and special magic, even the elves can only afford to do this by making boards for lots of people to get the volume up and the average cost per board down to less than a pot of gold.

Fortunately the elves have gone high tech and there are now quite a few places on the internet where you can upload Gerber and drill files and receive finished boards usually within a week or two, all without having to dig deep into your own pot of gold.  For example, you can get however many boards fit into 75 square inches for $250 at Gold Phoenix.  This includes solder mask on both sides, silk screen on one side, of course plated holes, and electrical testing.  8 layers will be more difficult since that is past most place's prototype process, but setting up your own process will be more difficult to.

This is a case where DIY really just doesn't make sense.  Are you going to refine your own silicon too?