The investigation was done or would be done

Hi there,

I am writing a thesis on the Syrian missile attack. I am confused by the tense of one sentence. The basic idea is that the missile attack to Syria by the US happened without any thorough investigation of the chemical attack in Syria. Should I say "the missile attack happened before any thorough investigation of the alleged government-led chemical attack in Syria would be done" or "the missile attack happened before any thorough investigation of the alleged government-led chemical attack in Syria had been done"?

Many thanks!