Earliest to use media after autoclaving?
There is a relatively simple (and yet logical) answer: You can use the media as soon as they are cold enough for your desired culture temperature. So if you want to use the media at 30°C, there is no need to wait longer. The media will only warm up again in the incubator until this temperature is reached.

The addition of antibiotics is also uncritical, since the media is ways to hot to be directly used when they still inactivate antibiotics. Your cells wouldn't survive this either.

There is also no waiting period necessary to use fresh media after autoclaving, since there are no processes going on when the autoclaving was done properly. If not, you will see contaminations pretty fast.