I’ve done this route both ways and it can be a bitch to get a ride. I waited 3 days in inyokern before giving up and getting a bus. Tied for my personal worst hitching wait ever.
In this heat? No fucking way, it would be stupid to try at anytime but dark, and good luck with that.
I would suggest hopping north to bakersfield, then hitching up via lake isabella to inyokern. Avoid getting dropped in inyokern if at all possible. But if you can’t there is a bus to lone pine for 19$ =\
Mammoth Lakes to Lancaster (395 South) - https://www.estransit.com/mammoth-lakes-to-lancaster-395-south
Are you going for the mountaineers route? If not you could literally hike out of lake isabella and follow the kern valley strait to the backside of the mountain, the PCT will get you to the same area aswell. A far more enjoyable journey, albeit longer.