She took her first steps in teaching while she was in the Peace Corps.
Literal
Peace Corps [in-に] being time [at-に] she [topic-は] teaching's first-step [object-を] stepped-out.
平和部隊 is 'Peace Corps.' 教職の第一歩を踏み出す is 'to take the first step in a teaching career' — 踏み出す literally means 'to step out/forward.' ~にいる頃に sets the temporal context: 'during the time she was in.' A sentence about career beginnings.