I'm new to this forum, and was wondering if I'm able to get an overnight permit for a group of 4 if I were to go to the station in the morning itself to pickup around 11am?

I've read some of the discussions here but don't seem to have a clear answer to this, I know you could obtain an unused permit for day hikes but how about the overnight permits? Im planning to hike sometime around May or June possibly a Sunday-Monday hike, whichever dates that are less likely to be full.

Any suggestions which months are the best to score unused overnight permits?