Why does capacitor voltage lag current?

So far I've established the following:

Current is the movement of charge over time, measured in coulombs/second.

Charge is the electron in an atom.

Voltage is the potential difference between two points and the energy per unit of charge.

Still, I don't understand why this happens:

How is it possible that at time t=0 the current is present in an RC circuit without the potential difference? What caused the charge to flow in the first place?