The electrons are just there. Think of the circuit as a system of pipes. The pipes are completely full with water, but without the battery connected the water doesn't move. Now, what happens if you suck on one side of the pipe (cause a pressure difference between the 'beginning' and 'end')? Water flows through the circuit. Same idea with the electrons in a circuit. Battery cell provides the potential difference (voltage) to cause electrons inside the wires to move through the circuit. Note: The electrons don't actually move that fast! They move around 10^-4 or 10^-5 m/s (I forget which order), but regardless, it's the same with water though. The important thing is that when you push on one side of the electrons in the wire, all of the electrons get pushed together since they're all squished together in the first place, and electrons don't like to get close to another more than they have to (same with nearly incompressible water!). Think: I suck on one side of the pipe in the water circuit (but not much) causing a small potential difference. The other side will almost immediately move, but the water in general wasn't moving that fast.
Hope this helps.