If you want to start in Washington, plan on starting around July 1 unless you’ve got some solid winter mountaineering experience, or 2010 is a very low snow year. Late May in a normal snow year will have the North Cascades choked with snow. In a freakishly low snow year like in 2005, late May would be possible, but you would have to bring a lot of route finding and hard snow travel skills with you, and plan to average a lot fewer miles (like 10). So, you’d need to haul a lot more food as well.
However, late May would be a fine time to start in SoCal. The heat really isn’t that bad, the water will still be there, and by the time you get to the Sierra conditions should be pretty good. It will be rather toasty crossing the Mojave, but this really isn’t a big deal.
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