The disk for Xbox game come from Singapore and I believe Sony are pressing their disk in the EU these days, at least for Australian consumers. North American stock is normally pressed in America. Given China's rather lax adherence to copyright most large IP holders don't press disk in China. Also, the factories that press disk are incredibly secure factories in order to avoid IP theft.
Game disk can be pressed months in advance to just days in advance depending on what the publisher wants. It's more common these days for disk to pressed a month or more in advance though because of day one patches. If what's on the game disk is broken or unfinished, no problem, just issue a day one patch.
Also, games are almost never finished on day one. They keep getting iterated on for weeks, months or years after launch so the disk is really nothing more than a key to allow access to the game for those that don't want to buy a digital copy and a shortcut to help the install process to go faster.
Also, I wouldn't assume a game like this would even have a disk version. It's possibly a digital-only release.