There is nothing to knock of a starting condition for the GOL until you put energy into it. There is no reason, for instance, you couldn't have a little robot moving the pebbles according to GOL rules. If you say the robot is the thing doing the computation the such is the case of the computer running this GOL simulation.

If you say it's not pebbles then imagine a mechanical computer built out of them. Provide some kinetic energy and rocks begin to compute just as the silicon in your computer begins to compute when you put electrical energy into it.

Nothing about the rules of GOL performs the necessary pattern transformations. You could say the pebbles follow the rules of GOL and put some energy into performing those transformations. This is what a computer does with GOL.

Your phone is just a drawing/design until you put energy into it as well. Then things start to "compute" due to the pattern of interactions that energy creates. There is no law of the universe that says this energy must be electrical.