Most people try to follow Jardine’s timetable and enter the Sierras from Kennedy Meadows around June 15. The only problem for you would be that there is a long stretch starting out to the first resupply at either Vermillion, Muir Trail Ranch or Kearsarge Pass.
I’m not sure how you would get a ride to Kennedy Meadow. IT would be easier to get a ride to Lone Pine and hike in at Cottonwood or Trail Pass, or start at Independence or if you want to take public transportation, then fly to SFO, catch a bus or train to Merced and the local bus to Yosemite and start there.
Spirit Walker