Congratulations to those who got their reservations!!
For those who didn't, here's the Unused Permits 2016
page. It has a link to the prior year, and each one goes back to the prior -- all the way to 2007.
If you look through those numbers, you can see that you can pretty easily walk-in the day before, especially mid-week, and pick up a free permit.
As for hiking in June, with this year's snow levels, the switchbacks may not be passable until mid-July. So people will instead be climbing the steep snow-slope just west of the switchbacks. Most people use crampons to do that, since it gives you a lot surer footing, and an ice axe is a good idea in case you slip, especially in late afternoons when the snow turns to ice on the descent.