Until projectile-mode-map prefix binding (e.g. C-c p p) has been called manually (i.e. without god-mode) at least once, the calling the enhanced binding with god-mode enabled (i.e. c SPC p p) does not work.

Once the prefix binding has been entered manually (without using god-mode) at least once, then calling it from god-mode with the enhanced binding starts to work too.

Choosing and executing one of the subcommands in the projectile-mode-map is not even necessary, it is enough to just enter the prefix binding (e.g. C-c p p) and then terminate the minibuffer with C-g.