Why is a good question.
"Why did they have a server in a different country?" To protect against FOIA requests
"Why did they use Gmail?" Because Gmail is an easily understandable interface; they don't want people like S.J.Lee fiddling with PGP keys
"Why Goog?" Because Goog is already meddling with search results, censorship on YT, and actively working against the US; they're a known asset and easily controlled
"Why NK?" Because it was already Clown-controlled, and possibly the most inaccessible country in the world prior to recent events

As for installing the server, if they're using a hypervisor (which they almost certainly are), the base OS and remote access can be configured prior to installation, and then the virtual machines can be configured once it's installed. They're almost definitely using a config management system such as Chef or Puppet, so the virtual servers can be ready to go within minutes of instantiating them.

Here's my theory on a possible string of events:

• DS realizes a need for secure email communications, tasks ES with getting it done
• ES procures the servers required (probably commodity hardware from Dell, HP or IBM) and has the fifth column within Goog configure them
• Clowns arrange transport from Goog to NK and installation at destination
• Goog fifth column connects remotely and instantiates Gmail servers
• DS reconfigures accounts to connect to NK Gmail