It was April 1905 when a school was built on the site of the old theater.
Literal
Theater-hut site-of-ruins [at-に] school [subject-が] was-built [nominalizer-の] [focus-が] 1905-year April was.
A cleft sentence using のが...でした to focus on when the school was built. 芝居小屋 (theater/playhouse) + 跡地 (former site) is a compound showing how Japanese builds location descriptions by stacking nouns. 建てられた is the passive of 建てる, used as a natural passive rather than adversative.