How to hardwire combined HVAC system for cooling?
A heat pump system has a valve that switches the system from heat to cool.  This is typically controlled by an orange wire, and based on how your nest was wired, it looks like your system follows that convention.

I'm not sure how common each type is, but some systems default to heat, and some default to cooling.  You hooked up the R wire to the Y and G and you got hot air, so we can assume yours defaults to heat.  Add the orange wire to your bundle and you should get cool air.  You need to wait some time when switching from heat to cool, so let the system set for 15-20 minutes if you've been messing with it and got hot air recently.