Can open circuits have 0 potential difference?
&quot;The switch is open for a very long time&quot; indicates that the capacitor will have had enough time to loose all charge (parasitic resistance, leakage current - both properties of all real capacitors).
That just means that \$V_c\$ will be 0 V right before \$t = 0\$.
I'm not sure that thinking in open circuits is helping here - a capacitor can be substituted with an open circuit in some cases, but this task is not one of them as it deals with the time domain analysis of the circuit.