。
She left home early in the morning so as not to miss the first train.
Literal
She [topic-は] first-departure train [target-に] not-be-late-boarding [so as to-ように] morning early home [object-を] left.
始発 ('first departure') is a standard rail-transport term, paired with 終電 ('last train') — both critical concepts in Japanese urban life given the country's dense, well-used rail network. 乗り遅れる ('miss boarding, miss the train') is a compound verb of 乗る ('board') + 遅れる ('be late'). The ~ないように pattern marks negative purpose: 'so as not to X.' 朝早く ('early in the morning') is a time adverbial with 早く as the i-adjective adverbial form. 家を出る uses を for the place left, a standard idiom for departure: '[exit] from home.'