It is possible that Mt. Goddard has never been climbed as a dayhike. The shortest approach is via
Lake Sabrina, but still requires 37 miles of hiking combined with nearly 8000 ft of elevation gain.
The easiest approach from the western side of the Sierras is probably via Florence Lake. This route
is 44 miles (if you don't take the ferry, it's another 10 miles) with 6330 ft of elevation gain.
Either way, it's one helluva day...
Camping is available at Lake Sabrina and Lake Florence.