Installing Origin and/or Steam games automatically in an unattended manner
Solution 1:
Steam
Valve provides CLI : https://developer.valvesoftware.com/wiki/SteamCMD
So it's possible to install games like this:
steamcmd +login anonymous +force_install_dir ../csgo_ds +app_update 740 +quit
Which logins to steam, creates custom folder and then installs CS:GO there.
This tool supports both Linux/MacOS and Windows, so you should be good automating your setup with it.
One limitation though, looks like it doesn't work for all the Steam games:
It works with games that use the SteamPipe content system.
Origin
I cannot find anything working right now, but in this answer author invested some time into Origin API.