Is it possible to have voltage across an inductor without having current through it?
Instantaneously, yes.  But that voltage will cause the current to ramp up according to the standard equation: \$V=L\frac{dI}{dt}\$

In other words, Voltage determines the rate-of-change of Current, which could easily pass through zero on its way to (theoretical) infinity.

(Theoretical because all inductors also have some resistance, which will ultimately limit the current to the standard resistive equation: \$V=IR\$)