I really don't see how anyone expects this to be over by June.

Exponential growth at the current rate would have it burning through the global population by the end of June, but since exponential growth becomes logistic growth after an appreciable fraction of the population is infected, June is probably closer to the halfway point than the end date.

And that's assuming zero curve flattening. The entire point of flattening the curve is to draw it out so that hospitals continue to function for longer. But this also makes the pandemic last longer.

A vaccine isn't expected for over a year, and even then, I'd expect at least a few months of logistical difficulties getting enough manufactured, distributed, and administered, especially given the state that hospitals will likely be in.