University men with literary ambitions were quick to turn to these theaters as offering a means of livelihood.

1. turn to：求助于；借助于；利用

2. as offering a means of livelihood 作宾语补足语，修饰 these theaters。

turn to sth. as... 类似于 use... as...（把......用作）的用法。为了化整为零，把该结构归到“观点类” 动词的结构类型：regard ...as...；think of...as...

【翻译】有文学抱负的大学生很快就把这些剧院作为谋生手段。