Just like bash in native unix environment, cygwin’s bash also support auto completion but somehow cygwyn doesn’t come with bash package. In my case the auto completion was not enabled yet, so I need to enable.
Check if you have /etc/bash_completion, then add it to your /etc/bash.bashrc
add this line
or you for your safety add conditional check beforehand
if [-f /etc/bash_completion]; then . /etc/bash_completion fi
restart you bash and try to use your magic tab key.