How long does it take to level up your Operation Payback coin in Counterstrike Global Offensive

Yes it is quite possible to do this. The issue is the game mode will not be enforced until a map change occurs. So for instance entering the following in the console will give the desired effect:

rcon_password fooBarBaz  
rcon game_mode 1 (classic competitive)  
rcon changelevel de_any 

This will change the game mode and change the current level thus enforcing the new game mode. Of note this is based on my NFO server config (nuclear fallout hosting)

From what I could find in the console you have to use:

MP_warmuptime 60

This would set the warmup time to 60 seconds. The standard is at 25 seconds and the minimum is 5 seconds.

Also as a tip for next time: in the console you can do find "text" and it will find all console commands with that text in it.