The existence of the giant clouds was virtually required for the Big Bang, first put forward in the 1920s, to maintain its reign as the dominant explanation of the cosmos.

【翻译】“宇宙大爆炸”理论是在20世纪20年代首次提出的，为了保持该理论能够解释宇宙的主导地位，巨大云团的存在（学说），无形中为“大爆炸理论”提供了必要的条件。

【分析】这是一个简单句：The existence of the giant clouds was virtually required for the Big Bang. 后面的两个成分一个是定语，一个是状语。

1. first put forward in the 1920s：过去分词短语作定语，修饰the Big Bang，相当于非限制性定语从句。可以提前单独翻译。

2. to maintain its reign as the dominant explanation of the cosmos：动词不定式短语作目的状语，可以提前翻译。

maintain its reign as ： “保持其作为......的主导地位”。

3. be required for：“为......提供必要的条件；是......的必要条件”。