No sooner had the sun risen at the foot of the mountain than he began climbing the mountain alone.
Literal
Mountain [attributive-の] foot [at-に] sun [subject-が] rise [as-soon-as-が早いか] just one-person mountain [object-を] began-to-climb.
Literary/narrative prose. ~が早いか ('as soon as, no sooner than') is a formal/literary conjunction indicating two events happening in immediate succession — literally 'is X early or (is Y)?', with the idea that the second event happens the instant the first does. 麓 ('foot of a mountain') is a specific geographical word. ただ一人 'alone, just one person.' 登り始める compound verb 'begin to climb.'