There are many alternatives out there for having an apt-like Package Manager for Cygwin (as well documented here) like:
But, as a challange, i didn't want to install anything and do everything i needed using only Cygwin inbuilt CLI commands.
On Cygwin FAQ webpage at chapter 2.3 you can find a list of all the parameters you can pass to the setup to automate things, like specify which architecture, proxy to use AND which packages to install or uninstall.