If you're in dire need of GS right away and can't get any new stock in time, at least cut out the centre 'touching' part which will have gone hard. I then roll out each individual colour with a round xacto knife handle to thin it out. Then put one layer on the other and start mixing/kneading as normal. It's tough on the fingers, but wet them with water to stop sticking to it.
I have to say putting GS in my mouth to 'start it off' sounds like something you should expect of a 5 years old?