[deadbeeves]

Chemical processes are not random, at least not in the way you're using the word. When you mix a base and an acid it's not subject to a roll of the dice whether they will neutralize or not. If you pour oil into water there's not a small chance that this one time they will dissolve into each other.

>We know that's what a cell is. But how do random chemical processes get there?

Work backwards. Think of the simplest cell you can. Now remove the membrane and the little molecular machines are free to wander in the medium arbitrarily far away from each other. The chemical processes are still happening, but they just take a long time to finish. All you need is for the abiotic medium to contain at least one of every of those molecules to have a sort of diffuse protolife.