In a normal year, a lot (most?) PCT thru-hikers go through starting sometime in June; I started NOBO through the Sierras in early June in 2008. Of course a lot depends on the snow year; 2008 wasn't too bad, but still a good deal of snow to walk over. I would expect you'll find lots of tracks to follow in the snow; hopefully most of them will even go where you want to ... :-)
25 mile days would be aggressive even for a person with light base weight and fully up to thru-hiker conditioning (NOBO PCT thru-hikers have walked 700 miles to get to the start of the Sierras). The snow, elevation gain and loss, perhaps elevation, all contribute to make it harder to make the miles there, though maybe by the time you're talking about in July the snow will be reduced somewhat (again, depending on the particular year). I wouldn't count on 25 mile days regardless, as who wants to race through such gorgeous country? I actually did a couple of 25 mile days in there, but more "it worked out that way", in one case pushing to get to town before the post office closed, and those were long and tiring days.