Question

If no current is passed through, why does the voltage start off negative?

Answer 1

There has to be net exchange of electrons for current to flow. As current flow from +ve terminal to -ve terminal , so this means electron from -ve terminal will leave through external circuit to reach the +ve terminal under emf . So equal no of electrons are supplied by +ve terminal to -ve terminal inside the battery. That completes the flow and hence we measure a physical current. 
If we consider only inside the battery there is a zero net exchange of electrons as emf is acting only in one direction. So for current to flow there has to be an external path.

Answer 2

From the standpoint of Physics, it’s negative to positive. The particle responsible for electricity, the electron, has a negative charge. In, for example, a battery, the negative power.