If you get everything you need for your brewday done ahead of time, i.e. sanitizing, cleaning, setting up, etc, then you can get a head start on your brewing and be able to pull the trigger anytime you want. Get your burner ready, keggle cleaned and covered, carboy filled with star san and covered, keep your airlocks in a tupperware of solution with a lid. These will all keep for a while as long as they're covered and in star san. When you find yourself with three hours, heat your water and go.
If you cut out the prep and cleaning time, our average brewday is three hours long (Mash/Sparge/Boil). We also batch sparge, so that may be cutting down some time as well. A copper chiller is a must, as well as a good mash tun that doesn't loose heat and sparges well. Good luck!